Finite Group DatabasebetaFinite Group DatabasebetaOrder 3776.
310 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 107 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×D59 |
| commutator, socle, cosocle | C22×C59 | C24 |
| Fitting | #124×C59 | C2 |
| hypercenter | #124 | D59 |
| hypocenter | C59 | #532 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745689 | C2 | semidirect |
| 2. C2×#11745687 | C2 | semidirect |
| 3. #14273725 | C2 | semidirect |
| 4. #14273723 | C2 | semidirect |
| 5. #14273715 | C2 | semidirect |
| 6. #14273700 | C2 | semidirect |
| 7. (C22⋊D59)⋊C4 | C2 | semidirect |
| 8. C42×D59 | C2 | semidirect |
| 9. #124×C59 | C2 | semidirect |
| 47. C4×D59 | D4 | semidirect |
| 61. Dic59 | #41 | semidirect |
| 68. C59 | #532 | semidirect |
| 74. #124 | D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745689 | 2 |
| C2×#11745687 | 2 |
| #14273725 | 2 |
| #14273723 | 2 |
| #14273715 | 2 |
| #14273700 | 2 |
| (C22⋊D59)⋊C4 | 2 |
| C42×D59 | 2 |
| #124×C59 | 2 |
| #532 | 59 |