Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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×#63243 | C2 | semidirect |
| 2. C2×D17⋊M16 | C2 | direct (N × H) |
| 3. C22×#63247 | C2 | semidirect |
| 4. C22×#63242 | C2 | semidirect |
| 15. C2×#63247 | C22 | semidirect |
| 16. C22×#3624 | C22 | semidirect |
| 17. D17⋊M16 | C22 | direct (N × H) |
| 18. C2×#63243 | C22 | semidirect |
| 19. C2×#63242 | C22 | semidirect |
| 40. #63247 | C23 | semidirect |
| 41. C2×#3624 | C23 | semidirect |
| 42. #63243 | C23 | semidirect |
| 43. #63242 | C23 | semidirect |
| 49. C22×D17 | M16 | semidirect |
| 67. #3624 | C24 | semidirect |
| 70. C22×C17 | C2×M16 | semidirect |
| 75. C2×D17 | C2×M16 | semidirect |
| 89. C2×C17 | C22×M16 | semidirect |
| 92. D17 | C22×M16 | semidirect |
| 107. C17 | C23×M16 | semidirect |
| 162. C22 | D17⋊M16 | direct (N × H) |
| 173. C2 | C2×D17⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| C2×D17⋊M16 | 2 |
| C22×#63247 | 2 |
| C22×#63242 | 2 |
| C23×C4×D17 | 2 |
| C23×M16 | 17 |