Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
360 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C2×C22⋊C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C22⋊C4 | #6923 |
| hypocenter | C61 | #1752 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14519832 | C2 | semidirect |
| 4. #16840628 | C2 | semidirect |
| 7. C22×#92420 | C4 | semidirect |
| 11. C22⋊#92420 | C4 | semidirect |
| 62. #92420 | C22⋊C4 | semidirect |
| 67. C22×C61 | #97 | semidirect |
| 91. C61 | #1752 | semidirect |
| 153. C22 | #14519832 | semidirect |