Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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×#11761613 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. C2×#14524014 | C2 | semidirect |
| 4. C2×#14523965 | C2 | semidirect |
| 5. C2×(C2×D67)⋊C8 | C2 | semidirect |
| 6. #16863158 | C2 | semidirect |
| 7. C2×#102×C67 | C2 | semidirect |
| 39. C2×D268 | D4 | semidirect |
| 54. C2×C67⋊C8 | D4 | semidirect |
| 56. C4⋊Dic67 | D4 | semidirect |
| 65. C2×D4×C67 | D4 | semidirect |
| 72. C4⋊C4×C67 | D4 | semidirect |
| 94. C22×D67 | D8 | semidirect |
| 172. C67 | #1999 | semidirect |
| 177. C2×#102 | D67 | semidirect |
| 221. C2×D4 | D268 | semidirect |
| 242. C4⋊C4 | C22⋊D67 | semidirect |