Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#10587476 | C2 | semidirect |
| 3. C4×#63223 | C2 | semidirect |
| 4. C4×C4⋊C4×C17 | C2 | semidirect |
| 12. #10587561 | C4 | semidirect |
| 13. #10587560 | C4 | semidirect |
| 16. #10587555 | C4 | semidirect |
| 44. #63223 | D4 | semidirect |
| 83. C4×C17 | #104 | semidirect |
| 90. C4×C4⋊C4 | D17 | semidirect |
| 113. C17 | #1980 | semidirect |
| 176. C4 | #10587476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| C2×#10587476 | 2 |
| C4×#63223 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #1980 | 17 |