Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 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 | C22 | #14524018 |
| commutator | C42×C67 | C23 |
| Frattini | C42 | C22×D67 |
| Fitting | #334×C67 | C2 |
| socle | C22×C67 | #121 |
| hypercenter | #334 | D67 |
| hypocenter | C67 | #1677 |
| LCS | G ▷ C42×C67 ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #334 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863743 | C2 | semidirect |
| 2. #16863687 | C2 | semidirect |
| 4. C8×D268 | C2 | semidirect |
| 5. #16863144 | C2 | semidirect |
| 6. #16863139 | C2 | semidirect |
| 7. #334×C67 | C2 | semidirect |
| 83. C67 | #1677 | semidirect |
| 88. #334 | D67 | semidirect |