Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #125×C61 | C2 |
| hypercenter | #125 | D61 |
| hypocenter | C61 | #553 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14519772 | C2 | semidirect |
| 2. #14519762 | C2 | semidirect |
| 3. #14519752 | C2 | semidirect |
| 4. #14519752 | C2 | semidirect |
| 5. #14519752 | C2 | semidirect |
| 6. C4×D244 | C2 | semidirect |
| 7. C4×D244 | C2 | semidirect |
| 8. #14519739 | C2 | semidirect |
| 9. #14519735 | C2 | semidirect |
| 10. C4⋊C4×D61 | C2 | semidirect |
| 11. #125×C61 | C2 | semidirect |
| 79. C61 | #553 | semidirect |
| 81. #125 | D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14519772 | 2 |
| #14519762 | 2 |
| #14519752 | 2 |
| C4×D244 | 2 |
| #14519739 | 2 |
| #14519735 | 2 |
| C4⋊C4×D61 | 2 |
| #125×C61 | 2 |
| #553 | 61 |