Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
576 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 242 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. #11763812 | C2 | direct (N × H) |
| 3. C2×#10587544 | C2 | semidirect |
| 4. C2×C4⋊#3624 | C2 | semidirect |
| 18. #10587544 | C22 | semidirect |
| 19. C4⋊#3624 | C22 | semidirect |
| 51. C2×C4×C17 | M16 | semidirect |
| 58. C2×Dic17 | M16 | semidirect |
| 79. C4×C17 | C2×M16 | semidirect |
| 83. Dic17 | C2×M16 | semidirect |
| 92. C2×C17 | #423 | semidirect |
| 110. C17 | C2×#423 | semidirect |
| 156. C2×C4 | #63247 | semidirect |
| 175. C4 | C2×#63247 | semidirect |
| 177. C2 | #11763812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| #11763812 | 2 |
| C2×#10587544 | 2 |
| C2×C4⋊#3624 | 2 |
| C22×C4×Dic17 | 2 |
| C2×#423 | 17 |