Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 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. #20260456 | C2 | semidirect |
| 4. C8×#11715895 | C2 | semidirect |
| 24. M16×C97 | C8 | semidirect |
| 40. C8×C97 | C2×C8 | semidirect |
| 43. #11715895 | M16 | direct (N × H) |
| 59. C97 | C8×M16 | semidirect |
| 79. M16 | #11715895 | direct (N × H) |
| 102. C8 | C2×#11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260788 | 2 |
| C2×C4×#11715895 | 2 |
| #20260456 | 2 |
| C8×#11715895 | 2 |
| C4×M16×C97 | 2 |
| C8×M16 | 97 |