Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#15690755 | C2 | semidirect |
| 3. #20261119 | C2 | semidirect |
| 4. C4×D776 | C2 | semidirect |
| 5. #20260540 | C2 | semidirect |
| 6. #20260537 | C2 | semidirect |
| 7. C4⋊C16×C97 | C2 | semidirect |
| 77. C97 | #2210 | semidirect |
| 82. C4⋊C16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| C2×D1552 | 2 |
| #20261119 | 2 |
| C4×D776 | 2 |
| #20260540 | 2 |
| #20260537 | 2 |
| C4⋊C16×C97 | 2 |
| #2210 | 97 |