Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
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. #20252848 | C2 | semidirect |
| 2. #20248335 | C2 | semidirect |
| 3. #20242056 | C2 | semidirect |
| 4. #20241883 | C2 | semidirect |
| 5. #20241778 | C2 | semidirect |
| 6. #20241290 | C2 | semidirect |
| 7. C47×#3205 | C2 | semidirect |
| 53. C4⋊(C47⋊C8) | D4 | semidirect |
| 64. C4⋊Q8×C47 | D4 | semidirect |
| 69. #127×C47 | D4 | semidirect |
| 76. C4⋊C8×C47 | D4 | semidirect |
| 117. C2×D188 | D8 | semidirect |
| 233. #3205 | D47 | semidirect |
| 271. C47 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D47 | semidirect |
| 292. #127 | C22⋊D47 | semidirect |
| 312. C4⋊C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252848 | 2 |
| #20248335 | 2 |
| #20242056 | 2 |
| #20241883 | 2 |
| #20241778 | 2 |
| #20241290 | 2 |
| C47×#3205 | 2 |
| #10238 | 47 |