Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 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. #11728823 | C2 | semidirect |
| 3. #11728822 | C2 | semidirect |
| 4. #11727748 | C2 | semidirect |
| 5. #11725581 | C2 | semidirect |
| 6. #11725581 | C2 | semidirect |
| 7. #11725495 | C2 | semidirect |
| 18. C2×#6392 | C22 | semidirect |
| 22. #89347 | C22 | semidirect |
| 23. C22⋊(C7⋊C16) | C22 | semidirect |
| 24. C22⋊(C7⋊C16) | C22 | semidirect |
| 298. C7 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3199 | 2 |
| #11728823 | 2 |
| #11728822 | 2 |
| #11727748 | 2 |
| #11725581 | 2 |
| #11725495 | 2 |
| #12284 | 7 |