Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 390 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. #19146316 | C2 | semidirect |
| 2. #19136850 | C2 | semidirect |
| 3. #19133947 | C2 | semidirect |
| 4. #19132645 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×#2206 | C2 | semidirect |
| 72. D8×C43 | D8 | semidirect |
| 147. #2206 | D43 | semidirect |
| 175. C43 | #12319 | semidirect |
| 228. D8 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146316 | 2 |
| #19136850 | 2 |
| #19133947 | 2 |
| #19132645 | 2 |
| #19132556 | 2 |
| #19132549 | 2 |
| C43×#2206 | 2 |
| #12319 | 43 |