Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic34 | C2 | semidirect |
| 5. #11762557 | C2 | semidirect |
| 6. #11762541 | C2 | semidirect |
| 7. C17×Q8⋊C8 | C2 | semidirect |
| 52. Q8×C17 | SD16 | semidirect |
| 69. Dic34 | SD16 | semidirect |
| 94. Q8⋊C8 | D17 | semidirect |
| 116. C17 | #1623 | semidirect |
| 148. Q8 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic34 | 2 |
| #11763182 | 2 |
| #11763010 | 2 |
| #11763009 | 2 |
| #11762557 | 2 |
| #11762541 | 2 |
| C17×Q8⋊C8 | 2 |
| #1623 | 17 |