Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D28 | C2 | semidirect |
| 2. #11728643 | C2 | semidirect |
| 3. #11726814 | C2 | semidirect |
| 4. #11726330 | C2 | semidirect |
| 5. C7×#1331 | C2 | semidirect |
| 6. #11725309 | C2 | semidirect |
| 7. #11725279 | C2 | semidirect |
| 18. #89467 | C22 | semidirect |
| 20. C4×C7×C16 | C22 | semidirect |
| 21. C7×#335 | C22 | semidirect |
| 24. C4⋊(C7⋊C16) | C22 | semidirect |
| 62. #1331 | D7 | semidirect |
| 82. C7×D8 | D8 | semidirect |
| 119. C4×C16 | C2×D7 | semidirect |
| 120. #335 | C2×D7 | semidirect |
| 151. D28 | D16 | semidirect |
| 237. D8 | D56 | semidirect |
| 296. C7 | #12316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D28 | 2 |
| #11728643 | 2 |
| #11726814 | 2 |
| #11726330 | 2 |
| C7×#1331 | 2 |
| #11725309 | 2 |
| #11725279 | 2 |
| #12316 | 7 |