Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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×D61 |
| commutator, socle, cosocle | C22×C61 | C24 |
| Fitting | #117×C61 | C2 |
| hypercenter | #117 | D61 |
| hypocenter | C61 | #535 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758222 | C2 | semidirect |
| 2. C22×D244 | C2 | semidirect |
| 3. #14519774 | C2 | semidirect |
| 4. #14519765 | C2 | semidirect |
| 5. #14519752 | C2 | semidirect |
| 6. #14519747 | C2 | semidirect |
| 7. #117×C61 | C2 | semidirect |
| 15. C2×D244 | C22 | semidirect |
| 16. C2×D244 | C22 | semidirect |
| 17. C2×C4×D61 | C22 | semidirect |
| 18. C2×Dic122 | C22 | semidirect |
| 19. C4⋊C4×C61 | C22 | semidirect |
| 21. C42×C61 | C22 | semidirect |
| 22. #11758198 | C22 | semidirect |
| 28. C2×C4×C61 | D4 | semidirect |
| 58. C61 | #535 | semidirect |
| 65. #117 | D61 | semidirect |
| 77. C4⋊C4 | C2×D61 | semidirect |
| 80. C42 | C2×D61 | semidirect |
| 94. C2×C4 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758222 | 2 |
| C22×D244 | 2 |
| #14519774 | 2 |
| #14519765 | 2 |
| #14519752 | 2 |
| #14519747 | 2 |
| #117×C61 | 2 |
| #535 | 61 |