Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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 | C23×#1181 |
| commutator, socle | C22×C29 | C23×C4 |
| Fitting, prime radical | C29×#121 | C4 |
| cosocle | C2×Dic29 | C24 |
| hypercenter | #121 | #1181 |
| hypocenter | C29 | #2967 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14272215 | C2 | semidirect |
| 2. #14272198 | C2 | semidirect |
| 3. #14272194 | C2 | semidirect |
| 4. #14272194 | C2 | semidirect |
| 5. #14272187 | C2 | semidirect |
| 6. #14272183 | C2 | semidirect |
| 7. #14272127 | C2 | semidirect |
| 8. C4×#90800 | C2 | semidirect |
| 148. C29 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272215 | 2 |
| #14272198 | 2 |
| #14272194 | 2 |
| #14272187 | 2 |
| #14272183 | 2 |
| #14272127 | 2 |
| C4×#90800 | 2 |
| #14271694 | 2 |
| #2967 | 29 |