Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19147697 | C2 | semidirect |
| 3. #19136332 | C2 | semidirect |
| 4. #19136330 | C2 | semidirect |
| 5. #19134638 | C2 | semidirect |
| 6. #19132702 | C2 | semidirect |
| 7. C43×#1386 | C2 | semidirect |
| 15. #14583158 | C4 | semidirect |
| 16. #14583153 | C4 | semidirect |
| 50. #13063265 | D4 | semidirect |
| 63. M32×C43 | D4 | semidirect |
| 182. #1386 | D43 | semidirect |
| 208. C43 | #13077 | semidirect |
| 238. M32 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147697 | 2 |
| #19144258 | 2 |
| #19136332 | 2 |
| #19136330 | 2 |
| #19134638 | 2 |
| #19132702 | 2 |
| C43×#1386 | 2 |
| #13077 | 43 |