Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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×#14583328 | C2 | semidirect |
| 2. C2×#14582738 | C2 | semidirect |
| 3. C2×#14582734 | C2 | semidirect |
| 4. #19136682 | C2 | semidirect |
| 5. #19132775 | C2 | semidirect |
| 6. (C2×D43)⋊C32 | C2 | semidirect |
| 7. C43×#1415 | C2 | semidirect |
| 32. Dic344 | D4 | semidirect |
| 43. D16×C43 | D4 | semidirect |
| 114. #1415 | D43 | semidirect |
| 137. C43 | #13663 | semidirect |
| 153. D16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583328 | 2 |
| C2×#14582738 | 2 |
| C2×#14582734 | 2 |
| #19136682 | 2 |
| #19132775 | 2 |
| (C2×D43)⋊C32 | 2 |
| C43×#1415 | 2 |
| #13663 | 43 |