Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863274 |
| commutator | C23×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #344×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #344 | D67 |
| hypocenter | C67 | #1914 |
| LCS | G ▷ C23×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864162 | C2 | semidirect |
| 3. #16863378 | C2 | semidirect |
| 4. C2×#14523959 | C2 | semidirect |
| 5. C2×#14523959 | C2 | semidirect |
| 6. #16863166 | C2 | semidirect |
| 7. #344×C67 | C2 | semidirect |
| 45. #11761612 | D4 | semidirect |
| 55. M16×C67 | D4 | semidirect |
| 115. C67 | #1914 | semidirect |
| 122. #344 | D67 | semidirect |
| 166. M16 | D268 | semidirect |