Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587594 | C2 | semidirect |
| 2. C2×#10587560 | C2 | semidirect |
| 3. C4×#63252 | C2 | semidirect |
| 4. #11763010 | C2 | semidirect |
| 5. #11763005 | C2 | semidirect |
| 6. #11762815 | C2 | semidirect |
| 7. C17×#423 | C2 | semidirect |
| 16. C2×D136 | C22 | semidirect |
| 17. C2×#63219 | C22 | semidirect |
| 21. C4×D68 | C22 | semidirect |
| 24. C4×Dic34 | C22 | semidirect |
| 25. C17×C4⋊C8 | C22 | semidirect |
| 26. #10587492 | C22 | semidirect |
| 32. #63252 | D4 | semidirect |
| 78. D68 | C2×D4 | semidirect |
| 82. Dic34 | C2×D4 | semidirect |
| 95. C4×C17 | AGL(1,ℤ/8) | semidirect |
| 105. #423 | D17 | semidirect |
| 129. C4⋊C8 | C2×D17 | semidirect |
| 131. C17 | #3038 | semidirect |
| 201. C4 | #10587594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587560 | 2 |
| C4×#63252 | 2 |
| #11763010 | 2 |
| #11763005 | 2 |
| #11762815 | 2 |
| C17×#423 | 2 |
| #3038 | 17 |