Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C2×#17989474 | C2 | semidirect |
| 4. #108×#64408 | C2 | semidirect |
| 5. #22624994 | C2 | semidirect |
| 6. #22624993 | C2 | semidirect |
| 18. #17989502 | C4 | semidirect |
| 19. #17989501 | C4 | semidirect |
| 25. #17988395 | C4 | semidirect |
| 26. #17988394 | C4 | semidirect |
| 27. #17988393 | C4 | semidirect |
| 28. #359×C73 | C4 | semidirect |
| 39. #14556664 | C2×C4 | semidirect |
| 41. #14556662 | C2×C4 | semidirect |
| 62. C2×#11924003 | C2×C4 | semidirect |
| 65. #14556527 | C2×C4 | semidirect |
| 68. C2×C16×C73 | C2×C4 | semidirect |
| 69. #108×C73 | C2×C4 | semidirect |
| 187. C73 | #12640 | semidirect |
| 206. #359 | #64408 | semidirect |
| 236. C2×C16 | C2×#64408 | semidirect |
| 241. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#64408 | 2 |
| D73⋊#359 | 2 |
| C2×#17989474 | 2 |
| #108×#64408 | 2 |
| #22624994 | 2 |
| #22624993 | 2 |
| #359×D73 | 2 |
| #12640 | 73 |