Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
244 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19136428 | C2 | semidirect |
| 2. C16×D172 | C2 | semidirect |
| 4. #19132665 | C2 | semidirect |
| 5. #19132551 | C2 | semidirect |
| 6. #19132551 | C2 | semidirect |
| 7. C43×#1311 | C2 | semidirect |
| 68. C16×C43 | D8 | semidirect |
| 81. D172 | M32 | semidirect |
| 115. #1311 | D43 | semidirect |
| 136. C43 | #12038 | semidirect |
| 184. C16 | D344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136428 | 2 |
| C16×D172 | 2 |
| C8×D344 | 2 |
| #19132665 | 2 |
| #19132551 | 2 |
| C43×#1311 | 2 |
| #12038 | 43 |