Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11761617 | C2 | semidirect |
| 2. C2×#14524022 | C2 | semidirect |
| 4. C2×#14523968 | C2 | semidirect |
| 5. C2×#14523965 | C2 | semidirect |
| 6. #16863159 | C2 | semidirect |
| 7. C2×C22⋊C8×C67 | C2 | semidirect |
| 35. C2×Dic134 | D4 | semidirect |
| 52. C4⋊Dic67 | D4 | semidirect |
| 70. C2×C8×C67 | D4 | semidirect |
| 77. C23×C67 | SD16 | semidirect |
| 158. C67 | #2000 | semidirect |
| 164. C2×C22⋊C8 | D67 | semidirect |
| 221. C2×C8 | C22⋊D67 | semidirect |
| 242. C23 | #11761617 | semidirect |