Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. C2×#10587478 | C2 | semidirect |
| 4. #11762571 | C2 | semidirect |
| 12. C22×#3622 | C4 | semidirect |
| 60. #3622 | C22⋊C4 | semidirect |
| 66. C22×C17 | #107 | semidirect |
| 101. C17 | #1808 | semidirect |
| 149. C22 | #10587478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3622 | 2 |
| C2×#10587478 | 2 |
| #11762669 | 2 |
| #11762571 | 2 |
| C17×#380 | 2 |
| #1808 | 17 |