Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22620399 | C2 | semidirect |
| 2. #22615783 | C2 | semidirect |
| 3. #22608554 | C2 | semidirect |
| 4. #22608478 | C2 | semidirect |
| 5. #22608374 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#3109 | C2 | semidirect |
| 55. C4×#10596831 | D4 | semidirect |
| 64. C4⋊Q8×C73 | D4 | semidirect |
| 65. #127×C73 | D4 | semidirect |
| 83. #97×C73 | D4 | semidirect |
| 229. #3109 | D73 | semidirect |
| 235. C73 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D73 | semidirect |
| 276. #127 | C22⋊D73 | semidirect |
| 306. #97 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620399 | 2 |
| #22615783 | 2 |
| #22608554 | 2 |
| #22608478 | 2 |
| #22608374 | 2 |
| #22607797 | 2 |
| C73×#3109 | 2 |
| #10018 | 73 |