Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11758564 | C2 | semidirect |
| 2. C2×Q16×C31 | C2 | semidirect |
| 3. #11758519 | C2 | semidirect |
| 4. #11758496 | C2 | semidirect |
| 5. #11758495 | C2 | semidirect |
| 6. Q16×D31 | C2 | semidirect |
| 7. #11758481 | C2 | semidirect |
| 8. #11758478 | C2 | semidirect |
| 66. C2×Q16 | D31 | semidirect |
| 68. C31 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758564 | 2 |
| C2×Q16×C31 | 2 |
| #11758519 | 2 |
| #11758496 | 2 |
| #11758495 | 2 |
| Q16×D31 | 2 |
| #11758481 | 2 |
| #11758478 | 2 |
| #578 | 31 |