Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22627125 | C2 | semidirect |
| 2. C2×#17989671 | C2 | semidirect |
| 3. #22626984 | C2 | semidirect |
| 4. #22626983 | C2 | semidirect |
| 9. #17989691 | C22 | semidirect |
| 11. #17989671 | C22 | semidirect |
| 53. #14556613 | C8 | semidirect |
| 57. Q16×D73 | C8 | semidirect |
| 59. D8×D73 | C8 | semidirect |
| 61. #135×C73 | C8 | semidirect |
| 97. Dic292 | C2×C8 | semidirect |
| 102. D584 | C2×C8 | semidirect |
| 110. Q16×C73 | C2×C8 | semidirect |
| 112. D8×C73 | C2×C8 | semidirect |
| 172. D73 | #1336 | semidirect |
| 178. C73 | C2×#1336 | semidirect |
| 202. #135 | #10596842 | semidirect |
| 249. Q16 | C2×#10596842 | semidirect |
| 256. D8 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627125 | 2 |
| C2×#17989671 | 2 |
| #22626984 | 2 |
| #22626983 | 2 |
| D73⋊#443 | 2 |
| C2×#1336 | 73 |