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. #19144059 | C2 | semidirect |
| 3. #19139541 | C2 | semidirect |
| 4. #19133262 | C2 | semidirect |
| 5. #19133091 | C2 | semidirect |
| 6. #19132497 | C2 | semidirect |
| 7. C43×#1478 | C2 | semidirect |
| 42. #13063325 | D4 | semidirect |
| 47. #13063322 | D4 | semidirect |
| 60. C4⋊(C43⋊C8) | D4 | semidirect |
| 75. C4⋊C8×C43 | D4 | semidirect |
| 87. C2×D4×C43 | D8 | semidirect |
| 238. #1478 | D43 | semidirect |
| 271. C43 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D43 | semidirect |
| 352. C2×D4 | D344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145515 | 2 |
| #19144059 | 2 |
| #19139541 | 2 |
| #19133262 | 2 |
| #19133091 | 2 |
| #19132497 | 2 |
| C43×#1478 | 2 |
| #10238 | 43 |