Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #19145172 | C2 | semidirect |
| 2. #19136870 | C2 | semidirect |
| 3. #19136818 | C2 | semidirect |
| 4. #19136678 | C2 | semidirect |
| 5. D16×Dic43 | C2 | semidirect |
| 6. C4×C16×D43 | C2 | semidirect |
| 7. C43×#2246 | C2 | semidirect |
| 75. C16×C43 | #41 | semidirect |
| 95. C4×D43 | D16 | semidirect |
| 119. #2246 | D43 | semidirect |
| 145. C43 | #33733 | semidirect |
| 198. C16 | #10621900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145172 | 2 |
| #19136870 | 2 |
| #19136818 | 2 |
| #19136678 | 2 |
| D16×Dic43 | 2 |
| C4×C16×D43 | 2 |
| C43×#2246 | 2 |
| #33733 | 43 |