Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20254303 | C2 | semidirect |
| 2. #20251782 | C2 | semidirect |
| 3. #20244217 | C2 | semidirect |
| 4. #20242056 | C2 | semidirect |
| 5. #20242055 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#3205 | C2 | semidirect |
| 48. C4⋊(C47⋊C8) | D4 | semidirect |
| 58. C4⋊Q8×C47 | D4 | semidirect |
| 63. #127×C47 | D4 | semidirect |
| 70. C4⋊C8×C47 | D4 | semidirect |
| 125. C4×Dic47 | D8 | semidirect |
| 204. #3205 | D47 | semidirect |
| 238. C47 | #10280 | semidirect |
| 250. C4⋊Q8 | C22⋊D47 | semidirect |
| 263. #127 | C22⋊D47 | semidirect |
| 276. C4⋊C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254303 | 2 |
| #20251782 | 2 |
| #20244217 | 2 |
| #20242056 | 2 |
| #20242055 | 2 |
| #20241220 | 2 |
| C47×#3205 | 2 |
| #10280 | 47 |