Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
616 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×D136 | C2 | semidirect |
| 2. C2×#10587616 | C2 | semidirect |
| 3. #11763045 | C2 | direct (N × H) |
| 4. C2×#10587489 | C2 | semidirect |
| 5. C2×#10587492 | C2 | semidirect |
| 6. C23×C8×C17 | C2 | semidirect |
| 13. C22×C8×C17 | C22 | semidirect |
| 15. #10587616 | C22 | semidirect |
| 19. C2×D136 | C22 | semidirect |
| 20. #10587492 | C22 | semidirect |
| 21. #10587489 | C22 | semidirect |
| 39. C2×C8×C17 | D4 | semidirect |
| 48. C23×C17 | D8 | semidirect |
| 71. C8×C17 | C2×D4 | semidirect |
| 78. C22×C17 | C2×D8 | semidirect |
| 91. C23×C8 | D17 | semidirect |
| 97. C2×C17 | #466 | semidirect |
| 110. C22×C8 | C2×D17 | semidirect |
| 117. C17 | C2×#466 | semidirect |
| 136. C2×C8 | C22⋊D17 | semidirect |
| 148. C23 | D136 | semidirect |
| 167. C8 | C2×C22⋊D17 | semidirect |
| 176. C22 | C2×D136 | semidirect |
| 187. C2 | #11763045 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| C2×#10587616 | 2 |
| #11763045 | 2 |
| C2×#10587489 | 2 |
| C2×#10587492 | 2 |
| C23×C8×C17 | 2 |
| C2×#466 | 17 |