Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C22×D4×C61 | C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | #2973 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840793 | C2 | semidirect |
| 2. #16840782 | C2 | semidirect |
| 3. #16840732 | C2 | semidirect |
| 4. C2×C22⋊#92420 | C2 | semidirect |
| 6. C2×#11758217 | C22 | semidirect |
| 7. C22×#92420 | C22 | semidirect |
| 8. #14519844 | C22 | semidirect |
| 10. C22⋊#92420 | C22 | semidirect |
| 11. C22⋊#92420 | C22 | semidirect |
| 12. #14519832 | C22 | semidirect |
| 50. C23×C61 | M16 | semidirect |
| 101. C61 | #2973 | semidirect |
| 146. C23 | #11758217 | semidirect |