Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #19136635 | C2 | semidirect |
| 3. Q16×C43⋊C8 | C2 | semidirect |
| 4. #19132664 | C2 | semidirect |
| 5. #19132642 | C2 | semidirect |
| 6. #19132641 | C2 | semidirect |
| 7. C43×#2207 | C2 | semidirect |
| 54. Q16×C43 | D8 | semidirect |
| 101. C43⋊C8 | SD32 | semidirect |
| 118. #2207 | D43 | semidirect |
| 144. C43 | #12425 | semidirect |
| 176. Q16 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136635 | 2 |
| #19134209 | 2 |
| Q16×C43⋊C8 | 2 |
| #19132664 | 2 |
| #19132642 | 2 |
| #19132641 | 2 |
| C43×#2207 | 2 |
| #12425 | 43 |