Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 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. #20252998 | C2 | semidirect |
| 3. C2×#15689377 | C2 | semidirect |
| 4. C2×#15688932 | C2 | semidirect |
| 5. #20245103 | C2 | semidirect |
| 6. C2×#15688904 | C2 | semidirect |
| 7. C47×#1386 | C2 | semidirect |
| 39. C2×Dic188 | D4 | semidirect |
| 46. C2×D376 | D4 | semidirect |
| 47. C2×D376 | D4 | semidirect |
| 75. M32×C47 | D4 | semidirect |
| 77. #107×C47 | D4 | semidirect |
| 80. #106×C47 | D4 | semidirect |
| 220. #1386 | D47 | semidirect |
| 251. C47 | #13316 | semidirect |
| 292. M32 | D188 | semidirect |
| 295. #107 | D188 | semidirect |
| 298. #106 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689561 | 2 |
| #20252998 | 2 |
| C2×#15689377 | 2 |
| C2×#15688932 | 2 |
| #20245103 | 2 |
| C2×#15688904 | 2 |
| C47×#1386 | 2 |
| #13316 | 47 |