Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×C4×D193 | C2 | semidirect |
| 3. #20259884 | C2 | direct (N × H) |
| 4. C2×#15690534 | C2 | semidirect |
| 5. C2×#15690532 | C2 | semidirect |
| 6. C2×#15690532 | C2 | semidirect |
| 7. C2×#15690532 | C2 | semidirect |
| 8. C2×C4⋊C4×C193 | C2 | semidirect |
| 16. C2×C4×D193 | C22 | semidirect |
| 17. #15690534 | C22 | semidirect |
| 18. #15690532 | C22 | semidirect |
| 19. #15690532 | C22 | semidirect |
| 20. #15690532 | C22 | semidirect |
| 24. C4⋊C4×C193 | C22 | semidirect |
| 63. C2×C193 | #123 | semidirect |
| 69. C193 | C2×#123 | semidirect |
| 75. C2×C4⋊C4 | D193 | semidirect |
| 91. C4⋊C4 | C2×D193 | semidirect |
| 135. C2 | #20259884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D772 | 2 |
| C22×C4×D193 | 2 |
| #20259884 | 2 |
| C2×#15690534 | 2 |
| C2×#15690532 | 2 |
| C2×C4⋊C4×C193 | 2 |
| C2×#123 | 193 |