Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
670 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 192 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. #22626328 | C2 | direct (N × H) |
| 18. C2×Dic584 | C4 | semidirect |
| 19. C2×#14556537 | C4 | semidirect |
| 20. Q32×D73 | C4 | semidirect |
| 23. C2×Q32×C73 | C4 | semidirect |
| 47. Dic584 | C2×C4 | semidirect |
| 48. #14556537 | C2×C4 | semidirect |
| 53. Q32×C73 | C2×C4 | semidirect |
| 129. C2×C73 | #2176 | semidirect |
| 131. D73 | #2176 | semidirect |
| 139. C73 | C2×#2176 | semidirect |
| 146. C2×Q32 | #64408 | semidirect |
| 175. Q32 | C2×#64408 | semidirect |
| 263. C2 | #22626328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#64408 | 2 |
| #22626328 | 2 |
| C2×#17989514 | 2 |
| C2×#17989500 | 2 |
| C2×#17989474 | 2 |
| C2×Q32×D73 | 2 |
| C2×#2176 | 73 |