Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#14583530 | C2 | semidirect |
| 3. #19133534 | C2 | direct (N × H) |
| 4. C2×#14582635 | C2 | semidirect |
| 5. C2×#14582625 | C2 | semidirect |
| 10. #14583530 | C22 | semidirect |
| 20. #14582635 | C22 | semidirect |
| 21. #14582625 | C22 | semidirect |
| 105. C22×C4×C43 | SD16 | semidirect |
| 181. C2×C4×C43 | C2×SD16 | semidirect |
| 231. C2×C43 | #1599 | semidirect |
| 257. C43 | C2×#1599 | semidirect |
| 341. C22×C4 | #10621883 | semidirect |
| 417. C2×C4 | C2×#10621883 | semidirect |
| 453. C2 | #19133534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583530 | 2 |
| C2×#14583050 | 2 |
| #19133534 | 2 |
| C2×#14582635 | 2 |
| C2×#14582625 | 2 |
| C2×C43×#394 | 2 |
| C2×#1599 | 43 |