Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#10587601 | C2 | semidirect |
| 3. C4⋊Q8×D17 | C2 | semidirect |
| 4. #11763200 | C2 | semidirect |
| 5. #11763189 | C2 | semidirect |
| 6. #11763188 | C2 | semidirect |
| 7. #11763181 | C2 | semidirect |
| 8. C4×#63218 | C2 | semidirect |
| 9. C17×#492 | C2 | semidirect |
| 59. #63218 | D4 | semidirect |
| 89. C4×C17 | #137 | semidirect |
| 102. #492 | D17 | semidirect |
| 130. C17 | #3152 | semidirect |
| 191. C4 | #10587601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587601 | 2 |
| #11763357 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763200 | 2 |
| #11763189 | 2 |
| #11763188 | 2 |
| #11763181 | 2 |
| C4×#63218 | 2 |
| C17×#492 | 2 |
| #3152 | 17 |