Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #20260973 | C2 | direct (N × H) |
| 4. C2×#15690744 | C2 | semidirect |
| 5. C2×#15690734 | C2 | semidirect |
| 6. C22×Q16×C97 | C2 | semidirect |
| 16. #15690744 | C22 | semidirect |
| 17. #15690734 | C22 | semidirect |
| 20. C2×Q16×C97 | C22 | semidirect |
| 48. C22×D97 | Q16 | semidirect |
| 75. C2×D97 | C2×Q16 | semidirect |
| 82. C2×C97 | #467 | semidirect |
| 88. C97 | C2×#467 | semidirect |
| 89. C22×Q16 | D97 | semidirect |
| 98. C2×Q16 | C2×D97 | semidirect |
| 171. C2 | #20260973 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D97 | 2 |
| C2×#15690786 | 2 |
| #20260973 | 2 |
| C2×#15690744 | 2 |
| C2×#15690734 | 2 |
| C22×Q16×C97 | 2 |
| C2×#467 | 97 |