Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11763207 | C2 | semidirect |
| 3. #11763206 | C2 | semidirect |
| 4. #11763205 | C2 | semidirect |
| 7. C17×#498 | C2 | semidirect |
| 42. C8×D17 | Q8 | semidirect |
| 56. C8×C17 | C2×Q8 | semidirect |
| 57. #3622 | C2×Q8 | semidirect |
| 72. #498 | D17 | direct (N × H) |
| 77. D17 | #498 | direct (N × H) |
| 94. C17 | C2×#498 | semidirect |
| 128. C8 | Q8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D17 | 2 |
| #11763207 | 2 |
| #11763206 | 2 |
| #11763205 | 2 |
| #106×D17 | 2 |
| C4×C8×D17 | 2 |
| C17×#498 | 2 |
| C2×#498 | 17 |