Order 1792.
1198 conjugacy classes of subgroups.
The subgroup lattice has 408 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11736491 | C2 | semidirect |
| 5. #11728278 | C2 | semidirect |
| 8. #11726728 | C2 | semidirect |
| 77. #6407 | Q8 | semidirect |
| 143. #1136 | C2×Q8 | semidirect |
| 207. Dic14 | #100 | semidirect |
| 380. C7 | Q8×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic14 | 2 |
| #11736491 | 2 |
| C7×#1800 | 2 |
| C4×#6407 | 2 |
| #11728278 | 2 |
| #11727817 | 2 |
| Dic7×#100 | 2 |
| #11726728 | 2 |
| Q8×#100 | 7 |