Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#14582946 | C2 | semidirect |
| 3. #19136324 | C2 | semidirect |
| 4. #19136322 | C2 | semidirect |
| 5. C2×#14582680 | C2 | semidirect |
| 6. #19132711 | C2 | semidirect |
| 7. C43×#1389 | C2 | semidirect |
| 57. #13063261 | D4 | semidirect |
| 68. #108×C43 | D4 | semidirect |
| 185. #1389 | D43 | semidirect |
| 211. C43 | #12998 | semidirect |
| 251. #108 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144205 | 2 |
| C2×#14582946 | 2 |
| #19136324 | 2 |
| #19136322 | 2 |
| C2×#14582680 | 2 |
| #19132711 | 2 |
| C43×#1389 | 2 |
| #12998 | 43 |