Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
436 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Frattini | C23 | C22×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | C4×C22⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×#92420 | C2 | semidirect |
| 3. #16840628 | C2 | semidirect |
| 6. #14519834 | C4 | direct (N × H) |
| 29. C2×C4×D61 | C8 | semidirect |
| 30. C2×C4×D61 | C8 | semidirect |
| 34. C2×#92420 | C2×C4 | semidirect |
| 82. C2×D61 | C4×C8 | semidirect |
| 85. C4×C61 | C22⋊C8 | semidirect |
| 87. Dic61 | C22⋊C8 | semidirect |
| 102. C61 | C4×C22⋊C8 | semidirect |
| 186. C4 | #14519834 | direct (N × H) |