Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10587494 | C2 | semidirect |
| 3. C4×#63223 | C2 | semidirect |
| 4. C17×#423 | C2 | semidirect |
| 33. #63223 | D4 | semidirect |
| 61. C4×C17 | #100 | semidirect |
| 66. #423 | D17 | semidirect |
| 85. C17 | #1965 | semidirect |
| 129. C4 | #10587494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| C2×#10587494 | 2 |
| C4×#63223 | 2 |
| C17×#423 | 2 |
| #1965 | 17 |