Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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. #20259944 | C2 | semidirect |
| 2. #20259868 | C2 | semidirect |
| 3. #20259814 | C2 | semidirect |
| 4. #20259813 | C2 | semidirect |
| 5. #120×C193 | C2 | semidirect |
| 13. C22⋊Dic193 | C22 | semidirect |
| 14. C24×C193 | C22 | semidirect |
| 18. C22⋊C4×C193 | C22 | semidirect |
| 20. C22×D193 | D4 | semidirect |
| 29. C2×Dic193 | D4 | semidirect |
| 34. C23×C193 | D4 | semidirect |
| 39. C2×C4×C193 | D4 | semidirect |
| 63. C193 | B(4,𝔽2) | semidirect |
| 67. #120 | D193 | semidirect |
| 70. C24 | C2×D193 | semidirect |
| 82. C22⋊C4 | C2×D193 | semidirect |
| 88. C23 | C22⋊D193 | semidirect |
| 103. C2×C4 | C22⋊D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259944 | 2 |
| #20259868 | 2 |
| #20259814 | 2 |
| #20259813 | 2 |
| #120×C193 | 2 |
| B(4,𝔽2) | 193 |