Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #19147729 | C2 | semidirect |
| 2. C2×#14583335 | C2 | semidirect |
| 3. #19136331 | C2 | semidirect |
| 4. #19136311 | C2 | semidirect |
| 5. #19135493 | C2 | semidirect |
| 6. #19132681 | C2 | semidirect |
| 7. C43×#3155 | C2 | semidirect |
| 38. C2×Dic172 | D4 | semidirect |
| 40. C2×D344 | D4 | semidirect |
| 51. #13063265 | D4 | semidirect |
| 53. C2×C43⋊C16 | D4 | semidirect |
| 213. #3155 | D43 | semidirect |
| 250. C43 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147729 | 2 |
| C2×#14583335 | 2 |
| #19136331 | 2 |
| #19136311 | 2 |
| #19135493 | 2 |
| #19132681 | 2 |
| C43×#3155 | 2 |
| #13334 | 43 |