Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
696 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 149 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×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #395×C67 | C2 |
| hypercenter | #395 | D67 |
| hypocenter | C67 | #2555 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524032 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. #16863313 | C2 | semidirect |
| 4. #16863306 | C2 | semidirect |
| 5. #16863297 | C2 | semidirect |
| 6. #16863286 | C2 | semidirect |
| 7. #16863274 | C2 | semidirect |
| 8. #16863243 | C2 | semidirect |
| 9. #395×C67 | C2 | semidirect |
| 57. (C2×D67)⋊C4 | D4 | semidirect |
| 143. C67 | #2555 | semidirect |
| 146. #395 | D67 | semidirect |