Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 864 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, socle, cosocle | C23×C29 | C24 |
| Fitting, prime radical | C22×#41×C29 | C2 |
| hypercenter | C22×#41 | D29 |
| hypocenter | C29 | #2406 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745297 | C2 | semidirect |
| 2. C22×#90779 | C2 | semidirect |
| 3. #14271082 | C2 | semidirect |
| 4. #14271077 | C2 | semidirect |
| 5. #14271043 | C2 | semidirect |
| 6. #14271036 | C2 | semidirect |
| 7. #14271026 | C2 | semidirect |
| 91. C2×Dic29 | #41 | semidirect |
| 146. C29 | #2406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745297 | 2 |
| C22×#90779 | 2 |
| #14271082 | 2 |
| #14271077 | 2 |
| #14271043 | 2 |
| #14271036 | 2 |
| #14271026 | 2 |
| C22×#41×C29 | 2 |
| #2406 | 29 |