Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 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. #19143183 | C2 | semidirect |
| 3. #19136331 | C2 | semidirect |
| 4. C2×#14582680 | C2 | semidirect |
| 5. #19132697 | C2 | semidirect |
| 6. #19132696 | C2 | semidirect |
| 7. C43×#2145 | C2 | semidirect |
| 12. #14583154 | C4 | semidirect |
| 13. #14583149 | C4 | semidirect |
| 54. #13063257 | C2×C4 | semidirect |
| 55. #13063257 | D4 | semidirect |
| 64. C2×Q16×C43 | C2×C4 | semidirect |
| 66. C2×D8×C43 | C2×C4 | semidirect |
| 73. #106×C43 | D4 | semidirect |
| 190. #2145 | D43 | semidirect |
| 219. C43 | #13008 | semidirect |
| 226. C2×Q16 | C4×D43 | semidirect |
| 228. C2×D8 | C4×D43 | semidirect |
| 264. #106 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144200 | 2 |
| #19143183 | 2 |
| #19136331 | 2 |
| C2×#14582680 | 2 |
| #19132697 | 2 |
| #19132696 | 2 |
| C43×#2145 | 2 |
| #13008 | 43 |