Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #19145063 | C2 | semidirect |
| 2. #19140447 | C2 | semidirect |
| 3. #19133218 | C2 | semidirect |
| 4. #19133142 | C2 | semidirect |
| 5. #19133038 | C2 | semidirect |
| 6. #19132461 | C2 | semidirect |
| 7. C43×#3109 | C2 | semidirect |
| 55. C4×C43⋊C8 | D4 | semidirect |
| 64. C4⋊Q8×C43 | D4 | semidirect |
| 65. #127×C43 | D4 | semidirect |
| 83. #97×C43 | D4 | semidirect |
| 222. #3109 | D43 | semidirect |
| 260. C43 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D43 | semidirect |
| 276. #127 | C22⋊D43 | semidirect |
| 306. #97 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145063 | 2 |
| #19140447 | 2 |
| #19133218 | 2 |
| #19133142 | 2 |
| #19133038 | 2 |
| #19132461 | 2 |
| C43×#3109 | 2 |
| #10018 | 43 |