Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 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×C4⋊C4×C29 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C22×C4⋊C4 | D29 |
| hypocenter | C29 | C2×#537 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90805 | C2 | semidirect |
| 2. #14271744 | C2 | direct (N × H) |
| 3. C2×#11745259 | C2 | semidirect |
| 4. C2×#11745257 | C2 | semidirect |
| 5. C2×#11745292 | C2 | semidirect |
| 6. C22×C4⋊C4×C29 | C2 | semidirect |
| 11. C2×#90805 | C22 | semidirect |
| 17. C2×C4⋊C4×C29 | C22 | semidirect |
| 18. #11745292 | C22 | semidirect |
| 21. #11745259 | C22 | semidirect |
| 22. #11745257 | C22 | semidirect |
| 26. C22×C4×C29 | D4 | semidirect |
| 58. C2×C4×C29 | C2×D4 | semidirect |
| 89. C22×C4⋊C4 | D29 | semidirect |
| 91. C2×C29 | #537 | semidirect |
| 110. C2×C4⋊C4 | C2×D29 | semidirect |
| 112. C29 | C2×#537 | semidirect |
| 128. C22×C4 | D116 | semidirect |
| 155. C2×C4 | C2×D116 | semidirect |
| 175. C2 | #14271744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| #14271744 | 2 |
| C2×#11745259 | 2 |
| C2×#11745257 | 2 |
| C2×#11745292 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C2×#537 | 29 |