Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C2×C4×Q8×C61 | C2 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | #3497 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519825 | C2 | semidirect |
| 2. #16840434 | C2 | semidirect |
| 3. Q8×D244 | C2 | semidirect |
| 4. #16840424 | C2 | semidirect |
| 5. #16840343 | C2 | semidirect |
| 6. #16840312 | C2 | semidirect |
| 7. C2×C4×Q8×C61 | C2 | semidirect |
| 26. C2×Q8×C61 | D4 | semidirect |
| 74. C4×C61 | 2−1+4 | semidirect |
| 88. C2×C4×Q8 | D61 | semidirect |
| 89. C61 | #3497 | semidirect |
| 112. C2×Q8 | D244 | semidirect |
| 157. C4 | #14519825 | semidirect |