Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×Dic466 | C2 | semidirect |
| 3. #28416185 | C2 | semidirect |
| 4. #28416165 | C2 | semidirect |
| 6. C8×#14272338 | C2 | semidirect |
| 24. #16836582 | C8 | direct (N × H) |
| 42. Dic466 | C2×C8 | semidirect |
| 48. #14272338 | C2×C8 | semidirect |
| 60. C8×C233 | SD16 | semidirect |
| 77. C233 | C8×SD16 | semidirect |
| 138. C8 | #16836582 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic466 | 2 |
| C4×#16836582 | 2 |
| #28416185 | 2 |
| #28416165 | 2 |
| D4⋊#14272338 | 2 |
| C8×#14272338 | 2 |
| C8×D4×C233 | 2 |
| C8×SD16 | 233 |