Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 136 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. C2×#6768 | C2 | semidirect |
| 2. C2×#6766 | C2 | semidirect |
| 3. C2×C8×D15 | C2 | semidirect |
| 4. C2×C5×#204 | C2 | semidirect |
| 5. C2×C3×#677 | C2 | semidirect |
| 6. C2×#6661 | C2 | semidirect |
| 7. C2×#6652 | C2 | semidirect |
| 8. #91276 | C2 | direct (N × H) |
| 20. #6768 | C22 | semidirect |
| 22. #6766 | C22 | semidirect |
| 25. C8×D15 | C22 | semidirect |
| 26. C5×#204 | C22 | semidirect |
| 27. C3×#677 | C22 | semidirect |
| 28. #6661 | C22 | semidirect |
| 29. #6652 | C22 | semidirect |
| 37. C2×#677 | D3 | semidirect |
| 68. C2×#204 | D5 | semidirect |
| 88. #677 | C2×D3 | semidirect |
| 121. #204 | C2×D5 | semidirect |
| 154. C2×C3×C5 | #135 | semidirect |
| 214. C3×C5 | C2×#135 | semidirect |
| 228. C2×C5 | #916 | semidirect |
| 256. C2×C3 | #4062 | semidirect |
| 260. C5 | C2×#916 | semidirect |
| 273. C3 | C2×#4062 | semidirect |
| 277. C2 | #91276 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6768 | 2 |
| C2×#6766 | 2 |
| C2×C8×D15 | 2 |
| C2×C5×#204 | 2 |
| C2×C3×#677 | 2 |
| C2×#6661 | 2 |
| C2×#6652 | 2 |
| #91276 | 2 |
| C2×#4062 | 3 |
| C2×#916 | 5 |