Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #19145515 | C2 | semidirect |
| 2. #19144061 | C2 | semidirect |
| 3. #19139537 | C2 | semidirect |
| 4. #19133264 | C2 | semidirect |
| 5. #19133089 | C2 | semidirect |
| 6. #19132985 | C2 | semidirect |
| 7. C43×#1303 | C2 | semidirect |
| 43. #13063325 | D4 | semidirect |
| 50. #13063322 | D4 | semidirect |
| 75. C4⋊C8×C43 | D4 | semidirect |
| 76. C4⋊C8×C43 | D4 | semidirect |
| 115. C2×D172 | D8 | semidirect |
| 239. #1303 | D43 | semidirect |
| 271. C43 | #10238 | semidirect |
| 311. C4⋊C8 | D172 | semidirect |
| 312. C4⋊C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145515 | 2 |
| #19144061 | 2 |
| #19139537 | 2 |
| #19133264 | 2 |
| #19133089 | 2 |
| #19132985 | 2 |
| C43×#1303 | 2 |
| #10238 | 43 |