Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #19146205 | C2 | semidirect |
| 2. #19136859 | C2 | semidirect |
| 3. #19134071 | C2 | semidirect |
| 4. #19132639 | C2 | semidirect |
| 5. #19132562 | C2 | semidirect |
| 6. #19132552 | C2 | semidirect |
| 7. C43×#2206 | C2 | semidirect |
| 19. #14582675 | C22 | semidirect |
| 20. #14582650 | C22 | semidirect |
| 23. C43×#493 | C22 | semidirect |
| 25. C43×C4⋊C16 | C22 | semidirect |
| 88. D8×C43 | D8 | semidirect |
| 175. #2206 | D43 | semidirect |
| 193. #493 | C2×D43 | semidirect |
| 201. C4⋊C16 | C2×D43 | semidirect |
| 206. C43 | #12324 | semidirect |
| 275. D8 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146205 | 2 |
| #19136859 | 2 |
| #19134071 | 2 |
| #19132639 | 2 |
| #19132562 | 2 |
| #19132552 | 2 |
| C43×#2206 | 2 |
| #12324 | 43 |