Finite Group DatabasebetaFinite Group DatabasebetaOrder 3776.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C22⋊Q8×C59 | C2 |
| hypercenter | C22⋊Q8 | D59 |
| hypocenter | C59 | #538 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14273722 | C2 | semidirect |
| 2. #14273716 | C2 | semidirect |
| 3. #14273712 | C2 | semidirect |
| 4. #14273702 | C2 | semidirect |
| 5. #14273701 | C2 | semidirect |
| 6. #14273697 | C2 | semidirect |
| 7. (C22⋊D59)⋊C4 | C2 | semidirect |
| 8. C2×(C2×D59)⋊C4 | C2 | semidirect |
| 9. C22⋊Q8×C59 | C2 | semidirect |
| 11. C2×Q8×C59 | C22 | semidirect |
| 17. C2×D236 | C22 | semidirect |
| 18. C2×C4×D59 | C22 | semidirect |
| 19. C4⋊C4×C59 | C22 | semidirect |
| 20. C4⋊C4×C59 | C22 | semidirect |
| 26. (C2×D59)⋊C4 | C22 | semidirect |
| 27. (C2×D59)⋊C4 | C22 | semidirect |
| 28. C4⋊Dic59 | C22 | semidirect |
| 29. Dic59⋊C4 | C22 | semidirect |
| 30. C4×Dic59 | C22 | semidirect |
| 75. C59 | #538 | semidirect |
| 79. C22⋊Q8 | D59 | semidirect |
| 86. C2×Q8 | C2×D59 | semidirect |
| 96. C4⋊C4 | C2×D59 | semidirect |
| 97. C4⋊C4 | C2×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14273722 | 2 |
| #14273716 | 2 |
| #14273712 | 2 |
| #14273702 | 2 |
| #14273701 | 2 |
| #14273697 | 2 |
| (C22⋊D59)⋊C4 | 2 |
| C2×(C2×D59)⋊C4 | 2 |
| C22⋊Q8×C59 | 2 |
| #538 | 59 |