Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C7×#3067 | C2 | semidirect |
| 2. C2×#89965 | C2 | semidirect |
| 3. #11741244 | C2 | semidirect |
| 4. #11729830 | C2 | semidirect |
| 5. #11729760 | C2 | semidirect |
| 6. C2×#89290 | C2 | semidirect |
| 7. #11725541 | C2 | semidirect |
| 44. C2×C7×Q16 | D4 | semidirect |
| 46. C2×C7×D8 | D4 | semidirect |
| 68. C7×#108 | D4 | semidirect |
| 79. #6386 | D4 | semidirect |
| 83. #3067 | D7 | semidirect |
| 228. C2×Q16 | C22⋊D7 | semidirect |
| 236. C2×D8 | C22⋊D7 | semidirect |
| 260. #108 | C22⋊D7 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3067 | 2 |
| C2×#89965 | 2 |
| #11741244 | 2 |
| #11729830 | 2 |
| #11729760 | 2 |
| C2×#89290 | 2 |
| #11725541 | 2 |
| #13310 | 7 |