Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
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. #31823184 | C2 | semidirect |
| 4. C8×#14555886 | C2 | semidirect |
| 24. M16×C281 | C8 | semidirect |
| 32. #14555886 | M16 | direct (N × H) |
| 43. C8×C281 | C2×C8 | semidirect |
| 58. C281 | C8×M16 | semidirect |
| 79. M16 | #14555886 | direct (N × H) |
| 102. C8 | C2×#14555886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823516 | 2 |
| C2×C4×#14555886 | 2 |
| #31823184 | 2 |
| C8×#14555886 | 2 |
| C4×M16×C281 | 2 |
| C8×M16 | 281 |