Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
374 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19146029 | C2 | semidirect |
| 2. #19136507 | C2 | semidirect |
| 3. #19135848 | C2 | semidirect |
| 4. #19132611 | C2 | semidirect |
| 5. #19132610 | C2 | semidirect |
| 6. #19132536 | C2 | semidirect |
| 7. C43×#2184 | C2 | semidirect |
| 168. #2184 | D43 | semidirect |
| 199. C43 | #12164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146029 | 2 |
| #19136507 | 2 |
| #19135848 | 2 |
| #19132611 | 2 |
| #19132610 | 2 |
| #19132536 | 2 |
| C43×#2184 | 2 |
| #12164 | 43 |