Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #28416514 | C2 | semidirect |
| 3. #28416185 | C2 | semidirect |
| 4. D4⋊#14272338 | C2 | semidirect |
| 5. #28416162 | C2 | semidirect |
| 6. #28416157 | C2 | semidirect |
| 7. #436×C233 | C2 | semidirect |
| 51. #14272338 | M16 | semidirect |
| 83. C233 | #1594 | semidirect |
| 87. #436 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16836579 | 2 |
| #28416514 | 2 |
| #28416185 | 2 |
| D4⋊#14272338 | 2 |
| #28416162 | 2 |
| #28416157 | 2 |
| #436×C233 | 2 |
| #1594 | 233 |