Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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. C4×#63243 | C2 | semidirect |
| 3. C42×#595 | C2 | semidirect |
| 4. #11763679 | C2 | semidirect |
| 11. C4×Q8×C17 | C4 | semidirect |
| 12. Q8×Dic17 | C4 | semidirect |
| 14. #10587579 | C4 | semidirect |
| 18. C4×D68 | C4 | semidirect |
| 21. #10587550 | C4 | direct (N × H) |
| 40. C4×#595 | C2×C4 | semidirect |
| 42. #63243 | C2×C4 | semidirect |
| 63. Q8×C17 | C42 | semidirect |
| 75. D68 | C42 | semidirect |
| 96. C4×C17 | #104 | semidirect |
| 101. Dic17 | #104 | semidirect |
| 116. C4×Q8 | #595 | semidirect |
| 131. C17 | C4×#104 | semidirect |
| 168. Q8 | C4×#595 | semidirect |
| 207. C4 | #10587550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587550 | 2 |
| C4×#63243 | 2 |
| C42×#595 | 2 |
| #11763679 | 2 |
| C4×#63256 | 2 |
| C4×#104 | 17 |