Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. #11763225 | C2 | semidirect |
| 2. #11763076 | C2 | semidirect |
| 3. #11762639 | C2 | semidirect |
| 4. #11762622 | C2 | semidirect |
| 5. C2×C17×D16 | C2 | semidirect |
| 51. C2×D16 | D17 | semidirect |
| 71. C17 | #2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763225 | 2 |
| #11763076 | 2 |
| #11762639 | 2 |
| #11762622 | 2 |
| C2×C17×D16 | 2 |
| #2221 | 17 |