Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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×C8 | C22×D67 |
| commutator, socle | C22×C67 | C22×C8 |
| Fitting | C4⋊C16×C67 | C2 |
| hypercenter | C4⋊C16 | D67 |
| hypocenter | C67 | #2164 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C4⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊(C67⋊C16) | C2 | semidirect |
| 5. #16863171 | C2 | semidirect |
| 6. C16×Dic67 | C2 | semidirect |
| 7. C4⋊C16×C67 | C2 | semidirect |
| 67. C67 | #2164 | semidirect |
| 70. C4⋊C16 | D67 | semidirect |