Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
576 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 2. #11763814 | C2 | direct (N × H) |
| 3. C2×#10587544 | C2 | semidirect |
| 15. #10587544 | C22 | semidirect |
| 42. C2×Dic17 | M16 | semidirect |
| 63. Dic17 | C2×M16 | semidirect |
| 70. C2×C17 | #423 | semidirect |
| 85. C17 | C2×#423 | semidirect |
| 136. C2 | #11763814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| #11763814 | 2 |
| C2×#10587544 | 2 |
| C2×C42×D17 | 2 |
| C2×#423 | 17 |