Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×#14582713 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. #19136310 | C2 | semidirect |
| 5. #19135344 | C2 | semidirect |
| 6. #19132676 | C2 | semidirect |
| 7. C43×#2140 | C2 | semidirect |
| 61. #107×C43 | D4 | semidirect |
| 165. #2140 | D43 | semidirect |
| 191. C43 | #13413 | semidirect |
| 225. #107 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583274 | 2 |
| C2×#14582713 | 2 |
| C2×#14582712 | 2 |
| #19136310 | 2 |
| #19135344 | 2 |
| #19132676 | 2 |
| C43×#2140 | 2 |
| #13413 | 43 |