Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
400 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #408×C67 | C2 |
| hypercenter | #408 | D67 |
| hypocenter | C67 | #2922 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863454 | C2 | semidirect |
| 3. #16863446 | C2 | semidirect |
| 4. #16863424 | C2 | semidirect |
| 5. #16863422 | C2 | semidirect |
| 7. M16×Dic67 | C2 | semidirect |
| 8. C2×C8×Dic67 | C2 | semidirect |
| 94. C67 | #2922 | semidirect |