Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D29 |
| commutator, cosocle | C22×C29 | C25 |
| Frattini | C22 | C24×D29 |
| Fitting | C22×#41×C29 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C22×#41 | D29 |
| hypocenter | C29 | C2×#550 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90809 | C2 | semidirect |
| 2. #14271832 | C2 | direct (N × H) |
| 3. C2×#11745302 | C2 | semidirect |
| 4. C2×#11745292 | C2 | semidirect |
| 5. C2×#11745300 | C2 | semidirect |
| 6. C2×Q8×Dic29 | C2 | semidirect |
| 7. C2×C4×C22⋊D29 | C2 | semidirect |
| 8. C22×#41×C29 | C2 | semidirect |
| 10. C2×#41×C29 | C22 | semidirect |
| 17. C2×#90809 | C22 | semidirect |
| 21. Q8×Dic29 | C22 | semidirect |
| 22. #11745302 | C22 | semidirect |
| 23. #11745300 | C22 | semidirect |
| 24. #11745292 | C22 | semidirect |
| 25. C4×C22⋊D29 | C22 | semidirect |
| 33. C2×Q8×C29 | D4 | semidirect |
| 67. Q8×C29 | C2×D4 | semidirect |
| 78. C2×Dic29 | #41 | semidirect |
| 101. Dic29 | C2×#41 | semidirect |
| 103. C22×#41 | D29 | semidirect |
| 111. C2×C29 | #550 | semidirect |
| 119. C2×#41 | C2×D29 | semidirect |
| 137. C29 | C2×#550 | semidirect |
| 142. C2×Q8 | C22⋊D29 | semidirect |
| 175. Q8 | C2×C22⋊D29 | semidirect |
| 211. C2 | #14271832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| #14271832 | 2 |
| C2×#11745302 | 2 |
| C2×#11745292 | 2 |
| C2×#11745300 | 2 |
| C2×Q8×Dic29 | 2 |
| C2×C4×C22⋊D29 | 2 |
| C22×#41×C29 | 2 |
| C2×#550 | 29 |