Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
576 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22620317 | C2 | semidirect |
| 2. #22620031 | C2 | semidirect |
| 4. #22608483 | C2 | semidirect |
| 5. #22608373 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#1533 | C2 | semidirect |
| 38. #14556591 | D4 | semidirect |
| 39. #14556591 | D4 | semidirect |
| 62. C4×#10596831 | D4 | semidirect |
| 81. #97×C73 | D4 | semidirect |
| 214. #1533 | D73 | semidirect |
| 218. C73 | #10022 | semidirect |
| 287. #97 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620317 | 2 |
| #22620031 | 2 |
| #22615784 | 2 |
| #22608483 | 2 |
| #22608373 | 2 |
| #22607797 | 2 |
| C73×#1533 | 2 |
| #10022 | 73 |