Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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×#10587532 | C2 | semidirect |
| 3. C2×C8×#595 | C2 | semidirect |
| 5. #11763674 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 14. C2×M16×C17 | C4 | semidirect |
| 15. C2×#63223 | C4 | semidirect |
| 18. C2×#63218 | C4 | semidirect |
| 19. C2×#63218 | C4 | semidirect |
| 22. C22⋊#3624 | C4 | semidirect |
| 24. #10587543 | C4 | semidirect |
| 75. C2×#595 | M16 | semidirect |
| 97. C8×C17 | C22⋊C4 | semidirect |
| 99. #3622 | C22⋊C4 | semidirect |
| 142. C2×M16 | #595 | semidirect |
| 155. C17 | #1753 | semidirect |
| 228. C8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763777 | 2 |
| C2×#10587532 | 2 |
| C2×C8×#595 | 2 |
| C4×C22⋊#595 | 2 |
| #11763674 | 2 |
| C2×M16×D17 | 2 |
| #1753 | 17 |