Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #19137705 | C2 | semidirect |
| 3. #19133218 | C2 | semidirect |
| 4. #19133103 | C2 | semidirect |
| 5. #19132488 | C2 | semidirect |
| 6. #19132487 | C2 | semidirect |
| 7. C43×#1505 | C2 | semidirect |
| 11. #14583291 | C4 | semidirect |
| 12. #14583286 | C4 | semidirect |
| 58. #13063236 | C2×C4 | semidirect |
| 66. C4⋊Q8×C43 | C2×C4 | semidirect |
| 67. #127×C43 | C2×C4 | semidirect |
| 224. #1505 | D43 | semidirect |
| 257. C43 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D43 | semidirect |
| 272. #127 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145063 | 2 |
| #19137705 | 2 |
| #19133218 | 2 |
| #19133103 | 2 |
| #19132488 | 2 |
| #19132487 | 2 |
| C43×#1505 | 2 |
| #9441 | 43 |