Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Fitting | C2×C29×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D29 |
| hypocenter | C29 | #3487 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90809 | C2 | semidirect |
| 2. #14271832 | C2 | semidirect |
| 3. #14271824 | C2 | semidirect |
| 4. #14271727 | C2 | semidirect |
| 5. #14271670 | C2 | semidirect |
| 6. #14271641 | C2 | semidirect |
| 7. C2×C29×2−1+4 | C2 | semidirect |
| 10. C2×#41×C29 | C22 | semidirect |
| 12. C22×Q8×C29 | C22 | semidirect |
| 17. #11745309 | C22 | semidirect |
| 18. #11745308 | C22 | semidirect |
| 19. Q8×Dic29 | C22 | semidirect |
| 20. #11745302 | C22 | semidirect |
| 21. #11745300 | C22 | semidirect |
| 24. #11745292 | C22 | semidirect |
| 25. C4×C22⋊D29 | C22 | semidirect |
| 31. C2×Q8×C29 | D4 | semidirect |
| 83. C2×2−1+4 | D29 | semidirect |
| 99. C2×#41 | C2×D29 | semidirect |
| 101. C22×Q8 | C2×D29 | semidirect |
| 114. C29 | #3487 | semidirect |
| 120. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| #14271832 | 2 |
| #14271824 | 2 |
| #14271727 | 2 |
| #14271670 | 2 |
| #14271641 | 2 |
| C2×C29×2−1+4 | 2 |
| #3487 | 29 |