Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #19135569 | C2 | semidirect |
| 5. #19132477 | C2 | semidirect |
| 6. #19132476 | C2 | semidirect |
| 7. C43×#1993 | C2 | semidirect |
| 12. #14583291 | C4 | semidirect |
| 57. #13063236 | C2×C4 | semidirect |
| 67. C4⋊Q8×C43 | C2×C4 | semidirect |
| 216. #1993 | D43 | semidirect |
| 250. C43 | #9003 | semidirect |
| 267. C4⋊Q8 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583291 | 2 |
| #19137766 | 2 |
| #19135569 | 2 |
| C2×#14582638 | 2 |
| #19132477 | 2 |
| #19132476 | 2 |
| C43×#1993 | 2 |
| #9003 | 43 |