Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 201 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, socle, cosocle | C23×C29 | C24 |
| Fitting | C2×C29×#121 | C2 |
| hypercenter | C2×#121 | D29 |
| hypocenter | C29 | #2856 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745302 | C2 | semidirect |
| 2. C2×#11745292 | C2 | semidirect |
| 3. C2×#11745301 | C2 | semidirect |
| 4. C22×C4×Dic29 | C2 | semidirect |
| 5. #14271066 | C2 | semidirect |
| 6. #14271064 | C2 | semidirect |
| 7. #14271063 | C2 | semidirect |
| 8. #14271032 | C2 | semidirect |
| 9. C2×C29×#121 | C2 | semidirect |
| 42. C22×C4×C29 | D4 | semidirect |
| 53. C22×Dic29 | D4 | semidirect |
| 69. C4×Dic29 | D4 | semidirect |
| 119. C22×C29 | #127 | semidirect |
| 132. C4×C29 | #121 | semidirect |
| 135. Dic29 | #121 | semidirect |
| 139. C2×#121 | D29 | semidirect |
| 175. C29 | #2856 | semidirect |
| 200. C22×C4 | C22⋊D29 | semidirect |
| 267. C22 | #11745302 | semidirect |
| 278. C4 | #11745301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| C2×#11745292 | 2 |
| C2×#11745301 | 2 |
| C22×C4×Dic29 | 2 |
| #14271066 | 2 |
| #14271064 | 2 |
| #14271063 | 2 |
| #14271032 | 2 |
| C2×C29×#121 | 2 |
| #2856 | 29 |