Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
616 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 274 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×#3624 | C2 | semidirect |
| 2. D4×#3624 | C2 | direct (N × H) |
| 3. C2×C4⋊#3624 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 5. C2×C4×#3624 | C2 | semidirect |
| 13. C22×#3624 | C22 | semidirect |
| 19. C22⋊#3624 | C22 | semidirect |
| 20. C4⋊#3624 | C22 | semidirect |
| 21. C4×#3624 | C22 | semidirect |
| 23. C2×D4×C17 | C8 | semidirect |
| 36. C2×#3624 | D4 | direct (N × H) |
| 46. C23×C17 | C2×C8 | semidirect |
| 49. D4×C17 | C2×C8 | semidirect |
| 50. C2×C4×C17 | C2×C8 | semidirect |
| 65. #3624 | C2×D4 | direct (N × H) |
| 72. C22×C17 | C22×C8 | semidirect |
| 75. C4×C17 | C22×C8 | semidirect |
| 88. C2×C17 | C8×D4 | semidirect |
| 107. C17 | C2×C8×D4 | semidirect |
| 109. C2×D4 | #3624 | direct (N × H) |
| 132. C23 | C2×#3624 | semidirect |
| 135. D4 | C2×#3624 | direct (N × H) |
| 147. C2×C4 | C2×#3624 | semidirect |
| 158. C22 | C22×#3624 | semidirect |
| 165. C4 | C22×#3624 | semidirect |
| 167. C2 | D4×#3624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3624 | 2 |
| D4×#3624 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×C4×#3624 | 2 |
| C2×D4×Dic17 | 2 |
| C2×C8×D4 | 17 |