Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #11763176 | C2 | semidirect |
| 4. #11763161 | C2 | semidirect |
| 5. #11763160 | C2 | semidirect |
| 6. #11763159 | C2 | semidirect |
| 9. C17×#487 | C2 | semidirect |
| 109. #487 | D17 | semidirect |
| 141. C17 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763176 | 2 |
| #11763161 | 2 |
| #11763160 | 2 |
| #11763159 | 2 |
| #11762816 | 2 |
| C4×#63218 | 2 |
| C17×#487 | 2 |
| #3139 | 17 |