Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#14583339 | C2 | semidirect |
| 2. C2×#14583175 | C2 | semidirect |
| 4. C2×#14582704 | C2 | semidirect |
| 5. C2×#14582682 | C2 | semidirect |
| 6. #19132705 | C2 | semidirect |
| 7. C2×C43×#359 | C2 | semidirect |
| 41. C2×Dic172 | D4 | semidirect |
| 59. #13063265 | D4 | semidirect |
| 80. #108×C43 | D4 | semidirect |
| 208. C2×#359 | D43 | semidirect |
| 242. C43 | #13308 | semidirect |
| 287. #108 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583339 | 2 |
| C2×#14583175 | 2 |
| #19144261 | 2 |
| C2×#14582704 | 2 |
| C2×#14582682 | 2 |
| #19132705 | 2 |
| C2×C43×#359 | 2 |
| #13308 | 43 |