Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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×#14583337 | C2 | semidirect |
| 3. #19145082 | C2 | semidirect |
| 4. #19136310 | C2 | semidirect |
| 5. #19135491 | C2 | semidirect |
| 6. #19132682 | C2 | semidirect |
| 7. C43×#2145 | C2 | semidirect |
| 41. C2×Dic172 | D4 | semidirect |
| 50. C2×D344 | D4 | semidirect |
| 66. C2×C43⋊C16 | D4 | semidirect |
| 82. M32×C43 | D4 | semidirect |
| 214. #2145 | D43 | semidirect |
| 250. C43 | #13334 | semidirect |
| 295. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147729 | 2 |
| C2×#14583337 | 2 |
| #19145082 | 2 |
| #19136310 | 2 |
| #19135491 | 2 |
| #19132682 | 2 |
| C43×#2145 | 2 |
| #13334 | 43 |