Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20253852 | C2 | semidirect |
| 2. #20253479 | C2 | semidirect |
| 3. #20242012 | C2 | semidirect |
| 4. #20241934 | C2 | semidirect |
| 5. #20241831 | C2 | semidirect |
| 6. #20241252 | C2 | semidirect |
| 7. C47×#2631 | C2 | semidirect |
| 42. #13094024 | D4 | semidirect |
| 43. #13094021 | D4 | semidirect |
| 58. #13093935 | D4 | semidirect |
| 59. C4×C47⋊C8 | D4 | semidirect |
| 223. #2631 | D47 | semidirect |
| 260. C47 | #10018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253852 | 2 |
| #20253479 | 2 |
| #20242012 | 2 |
| #20241934 | 2 |
| #20241831 | 2 |
| #20241252 | 2 |
| C47×#2631 | 2 |
| #10018 | 47 |