Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1502 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 267 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×#14583291 | C2 | semidirect |
| 2. C2×#14583289 | C2 | semidirect |
| 3. C2×#14583281 | C2 | semidirect |
| 4. C2×#14583273 | C2 | semidirect |
| 5. #19140701 | C2 | semidirect |
| 6. #19134282 | C2 | semidirect |
| 7. C43×#2658 | C2 | semidirect |
| 46. #13063236 | D4 | semidirect |
| 47. C4×C43⋊C8 | D4 | semidirect |
| 134. #2658 | D43 | semidirect |
| 159. C43 | #33307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583291 | 2 |
| C2×#14583289 | 2 |
| C2×#14583281 | 2 |
| C2×#14583273 | 2 |
| #19140701 | 2 |
| #19134282 | 2 |
| C43×#2658 | 2 |
| #33307 | 43 |