Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. #22626950 | C2 | direct (N × H) |
| 24. #14556664 | C8 | semidirect |
| 26. C2×#11924031 | C8 | semidirect |
| 32. C2×#11924003 | C8 | semidirect |
| 33. C16×D73 | C8 | semidirect |
| 35. C2×C16×C73 | C8 | semidirect |
| 47. #11924031 | C2×C8 | semidirect |
| 54. #11924003 | C2×C8 | semidirect |
| 56. C16×C73 | C2×C8 | semidirect |
| 85. C2×C73 | #1313 | semidirect |
| 87. D73 | #1313 | semidirect |
| 93. C73 | C2×#1313 | semidirect |
| 118. C2×C16 | #10596842 | semidirect |
| 145. C16 | C2×#10596842 | semidirect |
| 175. C2 | #22626950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989682 | 2 |
| C2×#17989671 | 2 |
| #22626950 | 2 |
| C2×#17989474 | 2 |
| C2×#1313 | 73 |