Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1450 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1450 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×#14583292 | C2 | semidirect |
| 2. C2×#14583278 | C2 | semidirect |
| 5. #19142991 | C2 | semidirect |
| 7. C4×#13063235 | C2 | semidirect |
| 8. C2×C43×#494 | C2 | semidirect |
| 51. #13063235 | D4 | semidirect |
| 141. C4×C43 | #497 | semidirect |
| 148. C2×#494 | D43 | semidirect |
| 179. C43 | #33305 | semidirect |
| 292. C4 | #14583292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583292 | 2 |
| C2×#14583278 | 2 |
| C2×#14583273 | 2 |
| C2×#14583272 | 2 |
| #19142991 | 2 |
| #19142953 | 2 |
| C4×#13063235 | 2 |
| C2×C43×#494 | 2 |
| #33305 | 43 |