Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#15690538 | C2 | semidirect |
| 3. C4⋊C4×D193 | C2 | semidirect |
| 4. #20259823 | C2 | semidirect |
| 5. #20259821 | C2 | semidirect |
| 6. #20259819 | C2 | semidirect |
| 7. #103×C193 | C2 | semidirect |
| 9. #15690556 | C4 | semidirect |
| 26. D772 | C2×C4 | semidirect |
| 35. Q8×C193 | C2×C4 | semidirect |
| 58. C193 | #417 | semidirect |
| 64. #103 | D193 | semidirect |
| 84. Q8 | C4×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690556 | 2 |
| C2×#15690538 | 2 |
| C4⋊C4×D193 | 2 |
| #20259823 | 2 |
| #20259821 | 2 |
| #20259819 | 2 |
| #103×C193 | 2 |
| #417 | 193 |