Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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×#15690545 | C2 | semidirect |
| 4. #20259824 | C2 | semidirect |
| 5. #20259823 | C2 | semidirect |
| 7. C2×Q16×C193 | C2 | semidirect |
| 45. C2×D193 | Q16 | semidirect |
| 57. C193 | #451 | semidirect |
| 61. C2×Q16 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D193 | 2 |
| C2×#15690545 | 2 |
| #20259875 | 2 |
| #20259824 | 2 |
| #20259823 | 2 |
| #20259811 | 2 |
| C2×Q16×C193 | 2 |
| #451 | 193 |