Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 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. #22616038 | C2 | semidirect |
| 3. #22608645 | C2 | semidirect |
| 4. #22608528 | C2 | semidirect |
| 5. #22608439 | C2 | semidirect |
| 6. #22607825 | C2 | semidirect |
| 7. C73×#3151 | C2 | semidirect |
| 47. C4⋊#10596831 | D4 | semidirect |
| 64. C4⋊Q8×C73 | D4 | semidirect |
| 69. #127×C73 | D4 | semidirect |
| 76. #97×C73 | D4 | semidirect |
| 213. #3151 | D73 | semidirect |
| 219. C73 | #10088 | semidirect |
| 256. C4⋊Q8 | C22⋊D73 | semidirect |
| 262. #127 | C22⋊D73 | semidirect |
| 286. #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 |
| #22616038 | 2 |
| #22608645 | 2 |
| #22608528 | 2 |
| #22608439 | 2 |
| #22607825 | 2 |
| C73×#3151 | 2 |
| #10088 | 73 |