Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D67 |
| commutator | C22×C67 | C2×C42 |
| Fitting | C2×#97×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×#97 | D67 |
| hypocenter | C67 | #1752 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14523953 | C2 | semidirect |
| 5. #16863151 | C2 | semidirect |
| 6. #16863150 | C2 | semidirect |
| 7. C2×#97×C67 | C2 | semidirect |
| 13. C2×C8×D67 | C4 | semidirect |
| 16. (C2×D67)⋊C8 | C4 | semidirect |
| 78. C8×C67 | C22⋊C4 | semidirect |
| 90. C2×D67 | #97 | semidirect |
| 105. C67 | #1752 | semidirect |
| 109. C2×#97 | D67 | semidirect |
| 185. C8 | (C2×D67)⋊C4 | semidirect |