Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22590565 | C2 | semidirect |
| 3. #22590474 | C2 | semidirect |
| 4. #22586385 | C2 | semidirect |
| 5. #22586300 | C2 | semidirect |
| 6. D4⋊(C71⋊C16) | C2 | semidirect |
| 7. C71×#1673 | C2 | semidirect |
| 16. C4⋊(C71⋊C16) | C22 | semidirect |
| 19. C4×C71⋊C16 | C22 | semidirect |
| 20. #500×C71 | C22 | semidirect |
| 23. #335×C71 | C22 | semidirect |
| 71. D568 | SD16 | semidirect |
| 155. #1673 | D71 | semidirect |
| 159. C71 | #12368 | semidirect |
| 162. #500 | C2×D71 | semidirect |
| 175. #335 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D568 | 2 |
| #22590565 | 2 |
| #22590474 | 2 |
| #22586385 | 2 |
| #22586300 | 2 |
| D4⋊(C71⋊C16) | 2 |
| C71×#1673 | 2 |
| #12368 | 71 |