Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×#15690749 | C2 | semidirect |
| 2. #20260968 | C2 | semidirect |
| 3. #20260563 | C2 | semidirect |
| 4. #20260536 | C2 | semidirect |
| 5. C2×D16×C97 | C2 | semidirect |
| 27. C16×C97 | D4 | semidirect |
| 56. C97 | #2218 | semidirect |
| 57. C2×D16 | D97 | semidirect |
| 83. C16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690749 | 2 |
| #20260968 | 2 |
| #20260563 | 2 |
| #20260536 | 2 |
| C2×D16×C97 | 2 |
| #2218 | 97 |