Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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 | #14524013 |
| commutator | C42×C67 | C23 |
| Frattini | C42 | C22×D67 |
| Fitting | Q8⋊C8×C67 | C2 |
| socle | C22×C67 | #120 |
| hypercenter | Q8⋊C8 | D67 |
| hypocenter | C67 | #1628 |
| LCS | G ▷ C42×C67 ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864119 | C2 | semidirect |
| 2. #16863743 | C2 | semidirect |
| 3. #16863596 | C2 | semidirect |
| 5. #16863143 | C2 | semidirect |
| 6. #16863125 | C2 | semidirect |
| 7. Q8⋊C8×C67 | C2 | semidirect |
| 96. C67 | #1628 | semidirect |
| 102. Q8⋊C8 | D67 | semidirect |