Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C67⋊#95 |
| commutator | C2×C4×C67 | C42 |
| Frattini | C23×C4 | C2×D67 |
| Fitting | #407×C67 | C2 |
| socle | C22×C67 | #95 |
| hypercenter | #407 | D67 |
| hypocenter | C67 | #1293 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 69. C67 | #1293 | semidirect |