Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1762 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1762 conjugacy classes of subgroups — too many to draw. Only its 299 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×#14583287 | C2 | semidirect |
| 2. C2×#14583275 | C2 | semidirect |
| 3. C2×#14583272 | C2 | semidirect |
| 4. C2×#14583271 | C2 | semidirect |
| 5. #19142989 | C2 | semidirect |
| 6. #19142951 | C2 | semidirect |
| 7. C4×#13063235 | C2 | semidirect |
| 8. C2×C43×#493 | C2 | semidirect |
| 52. #13063235 | D4 | semidirect |
| 53. C4×C43⋊C8 | D4 | semidirect |
| 66. C4×C8×C43 | D4 | semidirect |
| 139. C8×C43 | #127 | semidirect |
| 140. C43⋊C8 | #127 | semidirect |
| 154. C4×C43 | #496 | semidirect |
| 161. C2×#493 | D43 | semidirect |
| 194. C43 | #33304 | semidirect |
| 231. C4×C8 | C22⋊D43 | semidirect |
| 305. C8 | #13063321 | semidirect |
| 320. C4 | #14583287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583287 | 2 |
| C2×#14583275 | 2 |
| C2×#14583272 | 2 |
| C2×#14583271 | 2 |
| #19142989 | 2 |
| #19142951 | 2 |
| C4×#13063235 | 2 |
| C2×C43×#493 | 2 |
| #33304 | 43 |