Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
668 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14583341 | C2 | semidirect |
| 2. #19146337 | C2 | semidirect |
| 3. #19136856 | C2 | semidirect |
| 4. #19136709 | C2 | semidirect |
| 5. #19136657 | C2 | semidirect |
| 6. #19136530 | C2 | semidirect |
| 7. #19136521 | C2 | semidirect |
| 8. #19136428 | C2 | semidirect |
| 9. C4×Q32×C43 | C2 | semidirect |
| 69. Q32×C43 | D4 | semidirect |
| 167. C4×Q32 | D43 | semidirect |
| 200. C43 | #33843 | semidirect |
| 225. Q32 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583341 | 2 |
| #19146337 | 2 |
| #19136856 | 2 |
| #19136709 | 2 |
| #19136657 | 2 |
| #19136530 | 2 |
| #19136521 | 2 |
| #19136428 | 2 |
| C4×Q32×C43 | 2 |
| #33843 | 43 |