Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
620 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #384×C67 | C2 |
| hypercenter | #384 | D67 |
| hypocenter | C67 | #2538 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524023 | C2 | semidirect |
| 2. C2×C4×Dic134 | C2 | semidirect |
| 4. #16863318 | C2 | semidirect |
| 6. #16863295 | C2 | semidirect |
| 7. #16863253 | C2 | semidirect |
| 8. #384×C67 | C2 | semidirect |
| 31. C2×Dic134 | D4 | semidirect |
| 34. C2×D268 | Q8 | semidirect |
| 106. C4×C67 | C22⋊Q8 | semidirect |
| 119. C67 | #2538 | semidirect |
| 126. #384 | D67 | semidirect |
| 228. C4 | #14524023 | semidirect |