Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 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. #20245200 | C2 | semidirect |
| 2. #20241691 | C2 | semidirect |
| 3. #20241364 | C2 | semidirect |
| 4. #20241361 | C2 | semidirect |
| 7. #15688944 | C22 | semidirect |
| 11. #15688844 | C22 | semidirect |
| 12. C8×C47⋊C8 | C22 | semidirect |
| 59. Q16×C47 | M16 | semidirect |
| 63. D8×C47 | M16 | semidirect |
| 146. C47 | #11669 | semidirect |
| 184. Q16 | #10625329 | semidirect |
| 188. D8 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245200 | 2 |
| #20241691 | 2 |
| #20241364 | 2 |
| #20241361 | 2 |
| C47×#2956 | 2 |
| #11669 | 47 |