Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11726806 | C2 | semidirect |
| 3. #11726323 | C2 | semidirect |
| 4. C7×#1332 | C2 | semidirect |
| 5. #11725571 | C2 | semidirect |
| 6. #11725310 | C2 | semidirect |
| 7. #11725277 | C2 | semidirect |
| 67. #1332 | D7 | semidirect |
| 82. C7×Q16 | M16 | semidirect |
| 105. D56 | M16 | semidirect |
| 228. Q16 | #1131 | semidirect |
| 295. C7 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6482 | 2 |
| #11726806 | 2 |
| #11726323 | 2 |
| C7×#1332 | 2 |
| #11725571 | 2 |
| #11725310 | 2 |
| #11725277 | 2 |
| #11660 | 7 |