Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11762888 | C2 | semidirect |
| 3. #11762560 | C2 | semidirect |
| 4. #11762538 | C2 | semidirect |
| 5. C17×#322 | C2 | semidirect |
| 40. C8×C17 | M16 | semidirect |
| 56. #322 | D17 | semidirect |
| 71. C17 | #1594 | semidirect |
| 97. C8 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D136 | 2 |
| #11762888 | 2 |
| #11762560 | 2 |
| #11762538 | 2 |
| C17×#322 | 2 |
| #1594 | 17 |