Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
384 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×Dic172 | C2 | semidirect |
| 2. #19136851 | C2 | semidirect |
| 3. #19136636 | C2 | semidirect |
| 5. #19132645 | C2 | semidirect |
| 6. #19132560 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 89. Dic172 | D8 | semidirect |
| 98. D4×C43 | SD32 | semidirect |
| 147. D4⋊C16 | D43 | semidirect |
| 170. C43 | #12318 | semidirect |
| 254. D4 | #13063270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic172 | 2 |
| #19136851 | 2 |
| #19136636 | 2 |
| #19133950 | 2 |
| #19132645 | 2 |
| #19132560 | 2 |
| C43×D4⋊C16 | 2 |
| #12318 | 43 |