Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#15690532 | C2 | semidirect |
| 3. C2×#15690532 | C2 | semidirect |
| 4. #20259806 | C2 | semidirect |
| 5. C2×C4⋊C4×C193 | C2 | semidirect |
| 34. C2×C4×C193 | D4 | semidirect |
| 57. C193 | #394 | semidirect |
| 60. C2×C4⋊C4 | D193 | semidirect |
| 92. C2×C4 | D772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D772 | 2 |
| C2×#15690532 | 2 |
| #20259806 | 2 |
| C2×C4⋊C4×C193 | 2 |
| #394 | 193 |