Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 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×Q8×#595 | C2 | semidirect |
| 2. #11763761 | C2 | semidirect |
| 3. #11763751 | C2 | semidirect |
| 4. C4×C22⋊#595 | C2 | semidirect |
| 6. C2×#41×C17 | C4 | semidirect |
| 8. C2×#63256 | C4 | semidirect |
| 10. C2×#63254 | C4 | semidirect |
| 12. C2×#63252 | C4 | semidirect |
| 58. C2×#595 | #41 | semidirect |
| 59. Q8×C17 | C22⋊C4 | semidirect |
| 73. Dic34 | C22⋊C4 | semidirect |
| 110. C2×#41 | #595 | semidirect |
| 121. C17 | #2341 | semidirect |
| 155. Q8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| #11763761 | 2 |
| #11763751 | 2 |
| C4×C22⋊#595 | 2 |
| C2×#41×D17 | 2 |
| #2341 | 17 |