Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
546 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19141556 | C2 | semidirect |
| 2. #19135830 | C2 | semidirect |
| 3. #19135829 | C2 | semidirect |
| 5. #19132417 | C2 | semidirect |
| 6. #19132415 | C2 | semidirect |
| 7. C43×#1271 | C2 | semidirect |
| 107. C4⋊C4×C43 | D8 | semidirect |
| 227. #1271 | D43 | semidirect |
| 257. C43 | #7740 | semidirect |
| 350. C4⋊C4 | D344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19141556 | 2 |
| #19135830 | 2 |
| #19135829 | 2 |
| #19135668 | 2 |
| #19132417 | 2 |
| #19132415 | 2 |
| C43×#1271 | 2 |
| #7740 | 43 |