Order 1792.
1206 conjugacy classes of subgroups.
The subgroup lattice has 378 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11739749 | C2 | semidirect |
| 3. #11729378 | C2 | semidirect |
| 4. #11729356 | C2 | semidirect |
| 5. #11729325 | C2 | semidirect |
| 6. #11729306 | C2 | semidirect |
| 78. C2×C7×Q8 | M16 | semidirect |
| 95. C22×C4×C7 | M16 | semidirect |
| 252. C2×Q8 | #1136 | semidirect |
| 269. C22×C4 | #1136 | semidirect |
| 345. C7 | #17370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#520 | 2 |
| #11739749 | 2 |
| #11729378 | 2 |
| #11729356 | 2 |
| #11729325 | 2 |
| #11729306 | 2 |
| #17370 | 7 |