Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11763188 | C2 | semidirect |
| 4. #11762561 | C2 | semidirect |
| 5. #11762555 | C2 | semidirect |
| 6. #11762554 | C2 | semidirect |
| 46. D4×C17 | Q16 | semidirect |
| 101. C17 | #1669 | semidirect |
| 127. D4 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763188 | 2 |
| #11763089 | 2 |
| D4×#3622 | 2 |
| #11762561 | 2 |
| #11762555 | 2 |
| #11762554 | 2 |
| C17×#474 | 2 |
| #1669 | 17 |