Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×D752 | C2 | semidirect |
| 2. C2×#15689394 | C2 | semidirect |
| 3. #20253037 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20245103 | C2 | semidirect |
| 6. C2×#15688906 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 47. C2×D376 | D4 | semidirect |
| 70. C2×C16×C47 | D4 | semidirect |
| 72. #108×C47 | D4 | semidirect |
| 199. #1382 | D47 | semidirect |
| 228. C47 | #13319 | semidirect |
| 268. C2×C16 | D188 | semidirect |
| 270. #108 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D752 | 2 |
| C2×#15689394 | 2 |
| #20253037 | 2 |
| C2×#15688935 | 2 |
| #20245103 | 2 |
| C2×#15688906 | 2 |
| C47×#1382 | 2 |
| #13319 | 47 |