Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763575 | C2 | semidirect |
| 3. #11762815 | C2 | semidirect |
| 4. #11762813 | C2 | semidirect |
| 5. #11762782 | C2 | semidirect |
| 6. #11762565 | C2 | semidirect |
| 7. C17×H(3,ℤ/4) | C2 | semidirect |
| 20. #10587561 | C4 | semidirect |
| 21. #10587560 | C4 | semidirect |
| 44. C2×C8×C17 | D4 | semidirect |
| 57. C2×#3622 | D4 | semidirect |
| 116. H(3,ℤ/4) | D17 | semidirect |
| 140. C17 | #1910 | semidirect |
| 165. C2×C8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763575 | 2 |
| #11763378 | 2 |
| #11762815 | 2 |
| #11762813 | 2 |
| #11762782 | 2 |
| #11762565 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #1910 | 17 |