Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 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×#15690751 | C2 | semidirect |
| 2. #20261110 | C2 | semidirect |
| 3. D8×Dic97 | C2 | semidirect |
| 4. #20260553 | C2 | semidirect |
| 5. #20260537 | C2 | semidirect |
| 6. #20260536 | C2 | semidirect |
| 7. C2×D16×C97 | C2 | semidirect |
| 38. D8×C97 | D4 | semidirect |
| 74. Dic97 | D16 | semidirect |
| 82. C97 | #2206 | semidirect |
| 84. C2×D16 | D97 | semidirect |
| 115. D8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690751 | 2 |
| #20261110 | 2 |
| D8×Dic97 | 2 |
| #20260553 | 2 |
| #20260537 | 2 |
| #20260536 | 2 |
| C2×D16×C97 | 2 |
| #2206 | 97 |