Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
426 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 59 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. #19136545 | C2 | semidirect |
| 2. #19136540 | C2 | semidirect |
| 3. #19135662 | C2 | semidirect |
| 4. #19132583 | C2 | semidirect |
| 5. #19132580 | C2 | semidirect |
| 6. #19132531 | C2 | semidirect |
| 7. C43×#3197 | C2 | semidirect |
| 47. C2×Q16×C43 | D4 | semidirect |
| 49. C2×D8×C43 | D4 | semidirect |
| 62. #106×C43 | D4 | semidirect |
| 63. #106×C43 | D4 | semidirect |
| 189. #3197 | D43 | semidirect |
| 221. C43 | #12116 | semidirect |
| 229. C2×Q16 | C22⋊D43 | semidirect |
| 231. C2×D8 | C22⋊D43 | semidirect |
| 256. #106 | C22⋊D43 | semidirect |
| 257. #106 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136545 | 2 |
| #19136540 | 2 |
| #19135662 | 2 |
| #19132583 | 2 |
| #19132580 | 2 |
| #19132531 | 2 |
| C43×#3197 | 2 |
| #12116 | 43 |