Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16863273 |
| commutator | C23×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #413×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #413 | D67 |
| hypocenter | C67 | #1914 |
| LCS | G ▷ C23×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #413 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864163 | C2 | semidirect |
| 3. C2×#14523959 | C2 | semidirect |
| 4. #16863167 | C2 | semidirect |
| 5. #413×C67 | C2 | semidirect |
| 28. #11761612 | D4 | semidirect |
| 86. C67 | #1914 | semidirect |
| 89. #413 | D67 | semidirect |