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. #19146317 | C2 | semidirect |
| 2. #19136851 | C2 | semidirect |
| 3. #19136631 | C2 | semidirect |
| 4. #19133950 | C2 | semidirect |
| 5. #19132645 | C2 | semidirect |
| 6. #19132557 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 91. D344 | D8 | semidirect |
| 151. D4⋊C16 | D43 | semidirect |
| 175. C43 | #12319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146317 | 2 |
| #19136851 | 2 |
| #19136631 | 2 |
| #19133950 | 2 |
| #19132645 | 2 |
| #19132557 | 2 |
| C43×D4⋊C16 | 2 |
| #12319 | 43 |