Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#17989691 | C2 | semidirect |
| 2. #22627040 | C2 | semidirect |
| 3. #22626984 | C2 | semidirect |
| 4. #22626983 | C2 | semidirect |
| 9. #17989691 | C22 | semidirect |
| 10. #17989671 | C22 | semidirect |
| 53. #14556613 | C8 | semidirect |
| 57. Q16×D73 | C8 | semidirect |
| 59. D8×D73 | C8 | semidirect |
| 61. #135×C73 | C8 | semidirect |
| 177. C73 | #11604 | semidirect |
| 201. #135 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989691 | 2 |
| #22627040 | 2 |
| #22626984 | 2 |
| #22626983 | 2 |
| D73⋊#443 | 2 |
| #11604 | 73 |