Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#14582704 | C2 | semidirect |
| 5. #19135510 | C2 | semidirect |
| 6. #19132704 | C2 | semidirect |
| 7. C43×#1379 | C2 | semidirect |
| 12. #14583342 | C4 | semidirect |
| 39. C2×Dic172 | C2×C4 | semidirect |
| 65. M32×C43 | C2×C4 | semidirect |
| 182. #1379 | D43 | semidirect |
| 209. C43 | #13023 | semidirect |
| 238. M32 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583342 | 2 |
| #19143472 | 2 |
| C2×#14582707 | 2 |
| C2×#14582704 | 2 |
| #19135510 | 2 |
| #19132704 | 2 |
| C43×#1379 | 2 |
| #13023 | 43 |