Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 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. #19142548 | C2 | semidirect |
| 5. #19132420 | C2 | semidirect |
| 6. #19132419 | C2 | semidirect |
| 7. C43×#1271 | C2 | semidirect |
| 105. C4⋊C4×C43 | SD16 | semidirect |
| 208. #1271 | D43 | semidirect |
| 236. C43 | #7747 | semidirect |
| 327. C4⋊C4 | #10621873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19142548 | 2 |
| #19135830 | 2 |
| #19135829 | 2 |
| #19135685 | 2 |
| #19132420 | 2 |
| #19132419 | 2 |
| C43×#1271 | 2 |
| #7747 | 43 |