Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C61×#391 | C2 |
| hypercenter | #391 | D61 |
| hypocenter | C61 | #2431 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758226 | C2 | semidirect |
| 2. C2×#14519774 | C2 | semidirect |
| 3. C2×#14519766 | C2 | semidirect |
| 4. C2×#14519752 | C2 | semidirect |
| 5. #16839672 | C2 | semidirect |
| 6. #16839663 | C2 | semidirect |
| 7. #16839640 | C2 | semidirect |
| 8. C4×#11758198 | C2 | semidirect |
| 9. C61×#391 | C2 | semidirect |
| 38. C2×Q8×C61 | D4 | semidirect |
| 59. C2×D244 | D4 | semidirect |
| 65. C2×C4×D61 | D4 | semidirect |
| 100. C2×C4×C61 | #41 | semidirect |
| 154. #391 | D61 | semidirect |
| 158. C61 | #2431 | semidirect |
| 188. C2×Q8 | D244 | semidirect |
| 262. C2×C4 | #11758226 | semidirect |