Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 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. C2×#15689561 | C2 | semidirect |
| 2. C2×#15689394 | C2 | semidirect |
| 3. #20253060 | C2 | semidirect |
| 4. C2×#15688929 | C2 | semidirect |
| 5. C2×#15688923 | C2 | semidirect |
| 6. C2×#15688908 | C2 | semidirect |
| 7. C47×#1387 | C2 | semidirect |
| 50. C2×D376 | D4 | semidirect |
| 75. M32×C47 | D4 | semidirect |
| 78. #108×C47 | D4 | semidirect |
| 217. #1387 | D47 | semidirect |
| 249. C47 | #13307 | semidirect |
| 288. M32 | D188 | semidirect |
| 294. #108 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689561 | 2 |
| C2×#15689394 | 2 |
| #20253060 | 2 |
| C2×#15688929 | 2 |
| C2×#15688923 | 2 |
| C2×#15688908 | 2 |
| C47×#1387 | 2 |
| #13307 | 47 |