Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20256524 | C2 | semidirect |
| 2. #20253108 | C2 | semidirect |
| 3. #20253050 | C2 | semidirect |
| 4. C2×#15688934 | C2 | semidirect |
| 5. #20245117 | C2 | semidirect |
| 6. #20241487 | C2 | semidirect |
| 7. C47×#2117 | C2 | semidirect |
| 49. C2×Dic188 | D4 | semidirect |
| 53. C2×D376 | D4 | semidirect |
| 66. #13093960 | D4 | semidirect |
| 87. C2×C16×C47 | D4 | semidirect |
| 225. #2117 | D47 | semidirect |
| 259. C47 | #13318 | semidirect |
| 306. C2×C16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256524 | 2 |
| #20253108 | 2 |
| #20253050 | 2 |
| C2×#15688934 | 2 |
| #20245117 | 2 |
| #20241487 | 2 |
| C47×#2117 | 2 |
| #13318 | 47 |