Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 93 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. #19147729 | C2 | semidirect |
| 2. #19144177 | C2 | semidirect |
| 3. #19144172 | C2 | semidirect |
| 4. #19136332 | C2 | semidirect |
| 5. #19136205 | C2 | semidirect |
| 6. #19132696 | C2 | semidirect |
| 7. C43×#2145 | C2 | semidirect |
| 39. C2×Dic172 | D4 | semidirect |
| 41. C2×D344 | D4 | semidirect |
| 66. C2×C43⋊C16 | D4 | semidirect |
| 68. #13063257 | D4 | semidirect |
| 78. C2×Q16×C43 | D4 | semidirect |
| 80. C2×D8×C43 | D4 | semidirect |
| 87. #106×C43 | D4 | semidirect |
| 230. #2145 | D43 | semidirect |
| 265. C43 | #13309 | semidirect |
| 278. C2×Q16 | D172 | semidirect |
| 282. C2×D8 | D172 | semidirect |
| 316. #106 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147729 | 2 |
| #19144177 | 2 |
| #19144172 | 2 |
| #19136332 | 2 |
| #19136205 | 2 |
| #19132696 | 2 |
| C43×#2145 | 2 |
| #13309 | 43 |