Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14524000 |
| commutator | C2×C4×C67 | C22×C4 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | #347×C67 | C2 |
| socle | C2×C67 | #432 |
| hypercenter | #347 | D67 |
| hypocenter | C67 | #2165 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ #97 ◁ #347 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863216 | C2 | semidirect |
| 4. #16863174 | C2 | semidirect |
| 5. #347×C67 | C2 | semidirect |
| 52. C67 | #2165 | semidirect |
| 57. #347 | D67 | semidirect |