Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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×#3077 | C2 | semidirect |
| 2. #11740800 | C2 | semidirect |
| 4. #11729589 | C2 | semidirect |
| 5. #11729351 | C2 | semidirect |
| 6. #11728256 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 39. C7×C4⋊Q8 | D4 | semidirect |
| 40. C7×C4⋊Q8 | D4 | semidirect |
| 68. C7×C4⋊C8 | D4 | semidirect |
| 76. C4⋊(C7⋊C8) | D4 | semidirect |
| 80. #3077 | D7 | semidirect |
| 95. C2×C7×D4 | SD16 | semidirect |
| 226. C4⋊Q8 | C22⋊D7 | semidirect |
| 227. C4⋊Q8 | C22⋊D7 | semidirect |
| 256. C4⋊C8 | C22⋊D7 | semidirect |
| 316. C2×D4 | #1143 | semidirect |
| 408. C7 | #10246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3077 | 2 |
| #11740800 | 2 |
| #11739823 | 2 |
| #11729589 | 2 |
| #11729351 | 2 |
| #11728256 | 2 |
| #11725521 | 2 |
| #10246 | 7 |