Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863311 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #413×C67 | C2 |
| socle | C2×C67 | #394 |
| hypercenter | #413 | D67 |
| hypocenter | C67 | #2048 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #413 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863444 | C2 | semidirect |
| 3. #16863413 | C2 | semidirect |
| 4. #16863402 | C2 | semidirect |
| 5. C2×#14523959 | C2 | semidirect |
| 6. #16863167 | C2 | semidirect |
| 7. #413×C67 | C2 | semidirect |
| 111. C67 | #2048 | semidirect |
| 116. #413 | D67 | semidirect |