Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #20253940 | C2 | semidirect |
| 3. #20253211 | C2 | semidirect |
| 4. #20249333 | C2 | semidirect |
| 5. #20244599 | C2 | semidirect |
| 6. #20244368 | C2 | semidirect |
| 7. #20243600 | C2 | semidirect |
| 8. #20243201 | C2 | semidirect |
| 9. C47×#1965 | C2 | semidirect |
| 114. M16×C47 | #41 | semidirect |
| 201. #1965 | D47 | semidirect |
| 236. C47 | #25690 | semidirect |
| 314. M16 | #10625352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257262 | 2 |
| #20253940 | 2 |
| #20253211 | 2 |
| #20249333 | 2 |
| #20244599 | 2 |
| #20244368 | 2 |
| #20243600 | 2 |
| #20243201 | 2 |
| C47×#1965 | 2 |
| #25690 | 47 |