Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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. #19136852 | C2 | semidirect |
| 2. #19136635 | C2 | semidirect |
| 4. #19132644 | C2 | semidirect |
| 5. #19132559 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. D4×Q16×C43 | C2 | semidirect |
| 72. Q16×C43 | D8 | semidirect |
| 103. D4×C43 | SD32 | semidirect |
| 141. D4×Q16 | D43 | semidirect |
| 170. C43 | #12318 | semidirect |
| 218. Q16 | #10621882 | semidirect |
| 254. D4 | #13063268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136852 | 2 |
| #19136635 | 2 |
| #19133950 | 2 |
| #19132644 | 2 |
| #19132559 | 2 |
| D4⋊(C43⋊C16) | 2 |
| D4×Q16×C43 | 2 |
| #12318 | 43 |