Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1840 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×Dic34 | C2 | semidirect |
| 3. C2×#10587582 | C2 | direct (N × H) |
| 4. C22×#63225 | C2 | semidirect |
| 5. C22×#63225 | C2 | semidirect |
| 8. C22×C4⋊C4×C17 | C2 | semidirect |
| 19. C22×Dic34 | C22 | semidirect |
| 20. C2×C4⋊C4×C17 | C22 | semidirect |
| 23. C2×#63225 | C22 | semidirect |
| 24. C2×#63225 | C22 | semidirect |
| 25. #10587582 | C22 | direct (N × H) |
| 29. C23×D17 | Q8 | semidirect |
| 46. C2×Dic34 | C23 | semidirect |
| 47. C4⋊C4×C17 | C23 | semidirect |
| 50. #63225 | C23 | semidirect |
| 51. #63225 | C23 | semidirect |
| 59. C22×D17 | C2×Q8 | semidirect |
| 76. C22×C17 | C22⋊Q8 | semidirect |
| 84. C2×D17 | C22×Q8 | semidirect |
| 96. C22×C4⋊C4 | D17 | semidirect |
| 99. C2×C17 | C2×C22⋊Q8 | semidirect |
| 118. C2×C4⋊C4 | C2×D17 | semidirect |
| 121. C17 | C22×C22⋊Q8 | semidirect |
| 145. C4⋊C4 | C22×D17 | semidirect |
| 175. C22 | #10587582 | direct (N × H) |
| 187. C2 | C2×#10587582 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic34 | 2 |
| C23×C4×D17 | 2 |
| C2×#10587582 | 2 |
| C22×#63225 | 2 |
| C22×#63227 | 2 |
| C22×C4⋊C4×C17 | 2 |
| C22×C22⋊Q8 | 17 |