Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C4⋊C8×D233 | C2 | semidirect |
| 3. C4×#16836577 | C2 | semidirect |
| 4. #28416167 | C2 | semidirect |
| 5. #28416165 | C2 | semidirect |
| 6. D4⋊#14272338 | C2 | semidirect |
| 7. D4⋊C8×C233 | C2 | semidirect |
| 106. C233 | #1483 | semidirect |
| 114. D4⋊C8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416967 | 2 |
| C4⋊C8×D233 | 2 |
| C4×#16836577 | 2 |
| #28416167 | 2 |
| #28416165 | 2 |
| D4⋊#14272338 | 2 |
| D4⋊C8×C233 | 2 |
| #1483 | 233 |