Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #19145076 | C2 | semidirect |
| 3. #19136332 | C2 | semidirect |
| 4. #19136311 | C2 | semidirect |
| 5. #19135494 | C2 | semidirect |
| 6. #19132682 | C2 | semidirect |
| 7. C2×C43×#509 | C2 | semidirect |
| 58. C2×C43⋊C16 | D4 | semidirect |
| 71. C2×Q16×C43 | D4 | semidirect |
| 79. C2×D8×C43 | D4 | semidirect |
| 84. M32×C43 | D4 | semidirect |
| 212. C2×#509 | D43 | semidirect |
| 250. C43 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D43 | semidirect |
| 277. C2×D8 | C22⋊D43 | semidirect |
| 295. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147729 | 2 |
| #19145076 | 2 |
| #19136332 | 2 |
| #19136311 | 2 |
| #19135494 | 2 |
| #19132682 | 2 |
| C2×C43×#509 | 2 |
| #13334 | 43 |