Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #19147745 | C2 | semidirect |
| 2. #19136907 | C2 | semidirect |
| 3. C2×#14582738 | C2 | semidirect |
| 4. #19136716 | C2 | semidirect |
| 5. #19132787 | C2 | semidirect |
| 6. #19132736 | C2 | semidirect |
| 7. C43×#1417 | C2 | semidirect |
| 119. #1417 | D43 | semidirect |
| 143. C43 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147745 | 2 |
| #19136907 | 2 |
| C2×#14582738 | 2 |
| #19136716 | 2 |
| #19132787 | 2 |
| #19132736 | 2 |
| C43×#1417 | 2 |
| #13670 | 43 |