Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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. C22×#13094018 | C2 | semidirect |
| 2. #20251462 | C2 | direct (N × H) |
| 3. C2×#15689053 | C2 | semidirect |
| 4. C2×#15689045 | C2 | semidirect |
| 6. C2×C47×#384 | C2 | semidirect |
| 9. C2×#13094018 | C22 | semidirect |
| 14. #15689053 | C22 | semidirect |
| 15. #15689045 | C22 | semidirect |
| 22. C47×#384 | C22 | semidirect |
| 45. C2×C42×C47 | D4 | semidirect |
| 69. C42×C47 | C2×D4 | semidirect |
| 118. C2×#384 | D47 | semidirect |
| 119. C2×C47 | #2823 | semidirect |
| 137. #384 | C2×D47 | semidirect |
| 140. C47 | C2×#2823 | semidirect |
| 161. C2×C42 | D188 | semidirect |
| 191. C42 | C2×D188 | semidirect |
| 231. C2 | #20251462 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094018 | 2 |
| #20251462 | 2 |
| C2×#15689053 | 2 |
| C2×#15689045 | 2 |
| C2×#15689040 | 2 |
| C2×C47×#384 | 2 |
| C2×#2823 | 47 |