Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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. C22×D688 | C2 | semidirect |
| 2. C2×#14583169 | C2 | semidirect |
| 3. #19144243 | C2 | semidirect |
| 4. C2×#14582713 | C2 | semidirect |
| 5. #19136312 | C2 | semidirect |
| 6. #19132691 | C2 | semidirect |
| 7. C2×C43×#350 | C2 | semidirect |
| 45. C2×D344 | D4 | semidirect |
| 55. #13063261 | D4 | semidirect |
| 74. C2×C16×C43 | D4 | semidirect |
| 198. C2×#350 | D43 | semidirect |
| 228. C43 | #13319 | semidirect |
| 268. C2×C16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| C2×#14583169 | 2 |
| #19144243 | 2 |
| C2×#14582713 | 2 |
| #19136312 | 2 |
| #19132691 | 2 |
| C2×C43×#350 | 2 |
| #13319 | 43 |