Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting | C29×#391 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C22×D116 | C22 |
| hypercenter | #391 | D29 |
| hypocenter | C29 | #2372 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14271070 | C2 | semidirect |
| 3. #14271055 | C2 | semidirect |
| 4. #14271053 | C2 | semidirect |
| 6. C4×#90781 | C2 | semidirect |
| 7. #14271010 | C2 | semidirect |
| 8. #14271008 | C2 | semidirect |
| 9. C29×#391 | C2 | semidirect |
| 15. #11745309 | C4 | semidirect |
| 35. C2×Q8×C29 | C2×C4 | semidirect |
| 55. #90781 | C2×C4 | semidirect |
| 56. #90781 | C2×C4 | semidirect |
| 61. C4×Dic29 | C2×C4 | semidirect |
| 120. #391 | D29 | semidirect |
| 155. C29 | #2372 | semidirect |
| 159. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745309 | 2 |
| #14271070 | 2 |
| #14271055 | 2 |
| #14271053 | 2 |
| #14271041 | 2 |
| C4×#90781 | 2 |
| #14271010 | 2 |
| #14271008 | 2 |
| C29×#391 | 2 |
| #2372 | 29 |