Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #19143187 | C2 | semidirect |
| 3. C2×#14582709 | C2 | semidirect |
| 4. #19136224 | C2 | semidirect |
| 5. #19132711 | C2 | semidirect |
| 6. #19132694 | C2 | semidirect |
| 7. C43×#2145 | C2 | semidirect |
| 12. #14583171 | C4 | semidirect |
| 13. #14583166 | C4 | semidirect |
| 53. #13063261 | C2×C4 | semidirect |
| 65. C2×Q16×C43 | C2×C4 | semidirect |
| 67. C2×D8×C43 | C2×C4 | semidirect |
| 190. #2145 | D43 | semidirect |
| 222. C43 | #13005 | semidirect |
| 234. C2×Q16 | C4×D43 | semidirect |
| 236. C2×D8 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144311 | 2 |
| #19143187 | 2 |
| C2×#14582709 | 2 |
| #19136224 | 2 |
| #19132711 | 2 |
| #19132694 | 2 |
| C43×#2145 | 2 |
| #13005 | 43 |