Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 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. C2×#14583286 | C2 | semidirect |
| 2. #19142640 | C2 | semidirect |
| 3. #19135420 | C2 | semidirect |
| 4. C2×#14582639 | C2 | semidirect |
| 5. C2×#14582638 | C2 | semidirect |
| 6. #19132477 | C2 | semidirect |
| 7. C2×C43×#496 | C2 | semidirect |
| 53. #13063236 | D4 | semidirect |
| 70. #127×C43 | D4 | semidirect |
| 79. #97×C43 | D4 | semidirect |
| 226. C2×#496 | D43 | semidirect |
| 263. C43 | #10078 | semidirect |
| 286. #127 | C22⋊D43 | semidirect |
| 309. #97 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583286 | 2 |
| #19142640 | 2 |
| #19135420 | 2 |
| C2×#14582639 | 2 |
| C2×#14582638 | 2 |
| #19132477 | 2 |
| C2×C43×#496 | 2 |
| #10078 | 43 |