Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 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. #19144591 | C2 | semidirect |
| 2. #19144055 | C2 | semidirect |
| 3. #19139497 | C2 | semidirect |
| 4. #19133021 | C2 | semidirect |
| 5. #19132985 | C2 | semidirect |
| 6. #19132453 | C2 | semidirect |
| 7. C43×#1517 | C2 | semidirect |
| 63. C4⋊(C43⋊C8) | D4 | semidirect |
| 69. C4×C43⋊C8 | D4 | semidirect |
| 72. C4⋊Q8×C43 | D4 | semidirect |
| 73. #127×C43 | D4 | semidirect |
| 115. C2×D172 | D8 | semidirect |
| 252. #1517 | D43 | semidirect |
| 289. C43 | #9996 | semidirect |
| 302. C4⋊Q8 | D172 | semidirect |
| 303. #127 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144591 | 2 |
| #19144055 | 2 |
| #19139497 | 2 |
| #19133021 | 2 |
| #19132985 | 2 |
| #19132453 | 2 |
| C43×#1517 | 2 |
| #9996 | 43 |