Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14583342 | C2 | semidirect |
| 3. C2×#14583157 | C2 | semidirect |
| 4. C2×#14582710 | C2 | semidirect |
| 5. #19136316 | C2 | semidirect |
| 6. #19132701 | C2 | semidirect |
| 7. C2×C43×#349 | C2 | semidirect |
| 43. C2×Dic172 | D4 | semidirect |
| 62. #13063257 | D4 | semidirect |
| 78. M32×C43 | D4 | semidirect |
| 211. C2×#349 | D43 | semidirect |
| 242. C43 | #13317 | semidirect |
| 283. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583342 | 2 |
| #19144204 | 2 |
| C2×#14583157 | 2 |
| C2×#14582710 | 2 |
| #19136316 | 2 |
| #19132701 | 2 |
| C2×C43×#349 | 2 |
| #13317 | 43 |