Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22620914 | C2 | semidirect |
| 2. #22614870 | C2 | semidirect |
| 3. #22610851 | C2 | semidirect |
| 4. #22608530 | C2 | semidirect |
| 5. #22608374 | C2 | semidirect |
| 6. #22607786 | C2 | semidirect |
| 7. C73×#3109 | C2 | semidirect |
| 52. C4⋊#10596831 | D4 | semidirect |
| 65. C4⋊Q8×C73 | D4 | semidirect |
| 66. #127×C73 | D4 | semidirect |
| 84. #97×C73 | D4 | semidirect |
| 240. #3109 | D73 | semidirect |
| 246. C73 | #10004 | semidirect |
| 282. C4⋊Q8 | C22⋊D73 | semidirect |
| 283. #127 | C22⋊D73 | semidirect |
| 321. #97 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620914 | 2 |
| #22614870 | 2 |
| #22610851 | 2 |
| #22608530 | 2 |
| #22608374 | 2 |
| #22607786 | 2 |
| C73×#3109 | 2 |
| #10004 | 73 |