Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1296 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 147 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. #19134525 | C2 | semidirect |
| 3. C2×#14582623 | C2 | semidirect |
| 4. #19132473 | C2 | semidirect |
| 5. C43×#2315 | C2 | semidirect |
| 12. #14582808 | C4 | semidirect |
| 25. C22×D172 | C2×C4 | semidirect |
| 39. C43⋊#95 | C2×C4 | semidirect |
| 45. C2×C4⋊C4×C43 | D4 | semidirect |
| 135. C23×C43 | #102 | semidirect |
| 234. #2315 | D43 | semidirect |
| 263. C43 | #9017 | semidirect |
| 282. C2×C4⋊C4 | C22⋊D43 | semidirect |
| 402. C23 | #13063245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582808 | 2 |
| #19134525 | 2 |
| C2×#14582623 | 2 |
| #19132473 | 2 |
| C43×#2315 | 2 |
| #9017 | 43 |