Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#14583332 | C2 | semidirect |
| 2. #19145024 | C2 | semidirect |
| 3. #19136857 | C2 | semidirect |
| 4. #19136852 | C2 | semidirect |
| 5. #19136845 | C2 | semidirect |
| 6. C4×C16×D43 | C2 | semidirect |
| 7. C43×#2247 | C2 | semidirect |
| 42. C16×D43 | D4 | semidirect |
| 108. C4×C43 | #508 | semidirect |
| 117. #2247 | D43 | semidirect |
| 141. C43 | #33713 | semidirect |
| 226. C4 | #14583332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583332 | 2 |
| #19145024 | 2 |
| #19136857 | 2 |
| #19136852 | 2 |
| #19136845 | 2 |
| C4×C16×D43 | 2 |
| C43×#2247 | 2 |
| #33713 | 43 |