Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22×#13095486 | C2 | semidirect |
| 2. C2×#15690744 | C2 | semidirect |
| 3. #20260536 | C2 | direct (N × H) |
| 7. C2×#13095486 | C22 | semidirect |
| 9. #15690744 | C22 | semidirect |
| 13. C2×D8×C97 | C4 | semidirect |
| 28. D8×C97 | C2×C4 | semidirect |
| 63. C2×C97 | #357 | semidirect |
| 68. C97 | C2×#357 | semidirect |
| 76. C2×D8 | Dic97 | semidirect |
| 93. D8 | C2×Dic97 | semidirect |
| 131. C2 | #20260536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095486 | 2 |
| C2×#15690744 | 2 |
| #20260536 | 2 |
| C22×D8×C97 | 2 |
| C2×#357 | 97 |