Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×C7×#473 | C2 | semidirect |
| 2. C2×#89951 | C2 | semidirect |
| 4. C2×#89359 | C2 | semidirect |
| 5. C2×#89356 | C2 | semidirect |
| 6. C2×#89292 | C2 | semidirect |
| 7. #11725538 | C2 | semidirect |
| 43. C2×C7×Q16 | D4 | semidirect |
| 68. C7×#108 | D4 | semidirect |
| 77. #6386 | D4 | semidirect |
| 83. C2×#473 | D7 | semidirect |
| 232. C2×Q16 | C22⋊D7 | semidirect |
| 260. #108 | C22⋊D7 | semidirect |
| 396. C7 | #13308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#473 | 2 |
| C2×#89951 | 2 |
| #11741246 | 2 |
| C2×#89359 | 2 |
| C2×#89356 | 2 |
| C2×#89292 | 2 |
| #11725538 | 2 |
| #13308 | 7 |