Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C22×C4⋊C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C4⋊C4 | D67 |
| hypocenter | C67 | C2×#400 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863334 | C2 | direct (N × H) |
| 77. C2×C67 | #400 | semidirect |
| 84. C67 | C2×#400 | semidirect |
| 161. C2 | #16863334 | direct (N × H) |