Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1330 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14583641 | C2 | semidirect |
| 2. C2×#14583286 | C2 | semidirect |
| 3. #19133883 | C2 | direct (N × H) |
| 4. C2×#14582639 | C2 | semidirect |
| 5. C2×#14582638 | C2 | semidirect |
| 6. C2×C43×#496 | C2 | semidirect |
| 11. #14583641 | C22 | semidirect |
| 18. #14583286 | C22 | semidirect |
| 19. C2×#13063236 | C22 | semidirect |
| 20. #14582639 | C22 | semidirect |
| 21. #14582638 | C22 | semidirect |
| 24. C2×#127×C43 | C22 | semidirect |
| 27. C43×#496 | C22 | semidirect |
| 28. C2×#97×C43 | C22 | semidirect |
| 57. #13063236 | C23 | semidirect |
| 69. #127×C43 | C23 | semidirect |
| 76. #97×C43 | C23 | semidirect |
| 196. C2×#496 | D43 | semidirect |
| 202. C2×C43 | #1655 | semidirect |
| 213. C2×#127 | C2×D43 | semidirect |
| 223. #496 | C2×D43 | semidirect |
| 225. C2×#97 | C2×D43 | semidirect |
| 228. C43 | C2×#1655 | semidirect |
| 250. #127 | C22×D43 | semidirect |
| 276. #97 | C22×D43 | semidirect |
| 396. C2 | #19133883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583641 | 2 |
| C2×#14583286 | 2 |
| #19133883 | 2 |
| C2×#14582639 | 2 |
| C2×#14582638 | 2 |
| C2×C43×#496 | 2 |
| C2×#1655 | 43 |