Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
992 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14582694 | C2 | semidirect |
| 2. C2×#14582686 | C2 | semidirect |
| 3. #19135004 | C2 | semidirect |
| 4. #19134984 | C2 | semidirect |
| 17. C43×H(3,𝔽4) | C4 | semidirect |
| 68. C24×C43 | C22⋊C4 | semidirect |
| 75. C2×Q8×C43 | C22⋊C4 | semidirect |
| 102. C22⋊C4×C43 | C22⋊C4 | semidirect |
| 105. C42×C43 | C22⋊C4 | semidirect |
| 200. H(3,𝔽4) | Dic43 | semidirect |
| 216. C43 | #12763 | semidirect |
| 261. C24 | C22⋊Dic43 | semidirect |
| 268. C2×Q8 | C22⋊Dic43 | semidirect |
| 304. C22⋊C4 | C22⋊Dic43 | semidirect |
| 308. C42 | C22⋊Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582694 | 2 |
| C2×#14582686 | 2 |
| #19135004 | 2 |
| #19134984 | 2 |
| C2×C43×H(3,𝔽4) | 2 |
| #12763 | 43 |