Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C4 | C23×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C22×M32 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519852 | C2 | semidirect |
| 2. D61⋊M32 | C2 | direct (N × H) |
| 3. C2×#14519851 | C2 | semidirect |
| 4. C2×D61⋊C16 | C2 | semidirect |
| 6. #14519852 | C22 | semidirect |
| 7. #14519851 | C22 | semidirect |
| 8. D61⋊C16 | C22 | semidirect |
| 9. C2×#11758187 | C22 | semidirect |
| 41. #11758187 | C23 | semidirect |
| 70. C2×D61 | M32 | semidirect |
| 80. C2×C61 | C2×M32 | semidirect |
| 83. D61 | C2×M32 | semidirect |
| 89. C61 | C22×M32 | semidirect |
| 165. C2 | D61⋊M32 | direct (N × H) |