Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
700 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 700 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 |
|---|---|---|
| 2. #19137706 | C2 | semidirect |
| 3. C2×#14582695 | C2 | semidirect |
| 4. #19134554 | C2 | semidirect |
| 5. #19132722 | C2 | semidirect |
| 6. #19132721 | C2 | semidirect |
| 7. C43×#1793 | C2 | semidirect |
| 11. #14583072 | C4 | semidirect |
| 59. #13063244 | C2×C4 | semidirect |
| 68. 2−1+4×C43 | C2×C4 | semidirect |
| 262. #1793 | D43 | semidirect |
| 294. C43 | #13057 | semidirect |
| 299. 2−1+4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583072 | 2 |
| #19137706 | 2 |
| C2×#14582695 | 2 |
| #19134554 | 2 |
| #19132722 | 2 |
| #19132721 | 2 |
| C43×#1793 | 2 |
| #13057 | 43 |