Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
248 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11763893 | C2 | direct (N × H) |
| 16. C2×#3624 | C8 | semidirect |
| 20. #63242 | C8 | semidirect |
| 22. C2×C8×C17 | C8 | semidirect |
| 23. C2×#3622 | C8 | semidirect |
| 24. C8×D17 | C8 | semidirect |
| 37. #3624 | C2×C8 | semidirect |
| 38. C8×C17 | C2×C8 | semidirect |
| 39. #3622 | C2×C8 | semidirect |
| 54. C2×C17 | #322 | semidirect |
| 56. D17 | #322 | semidirect |
| 66. C17 | C2×#322 | semidirect |
| 77. C2×C8 | #3633 | semidirect |
| 94. C8 | C2×#3633 | semidirect |
| 107. C2 | #11763893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#3633 | 2 |
| #11763893 | 2 |
| C2×C8×#595 | 2 |
| C2×#322 | 17 |