Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#14582713 | C2 | semidirect |
| 3. #19136332 | C2 | semidirect |
| 4. #19136324 | C2 | semidirect |
| 5. #19136312 | C2 | semidirect |
| 6. #19134719 | C2 | semidirect |
| 7. C43×#2110 | C2 | semidirect |
| 13. #14583283 | C4 | semidirect |
| 14. #14583276 | C4 | semidirect |
| 62. M32×C43 | D4 | semidirect |
| 64. C2×C16×C43 | D4 | semidirect |
| 174. #2110 | D43 | semidirect |
| 201. C43 | #13215 | semidirect |
| 233. M32 | D172 | semidirect |
| 235. C2×C16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145081 | 2 |
| C2×#14582713 | 2 |
| #19136332 | 2 |
| #19136324 | 2 |
| #19136312 | 2 |
| #19134719 | 2 |
| C43×#2110 | 2 |
| #13215 | 43 |