Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22625869 | C2 | semidirect |
| 4. #22625854 | C2 | semidirect |
| 5. #22624808 | C2 | semidirect |
| 6. #22624808 | C2 | semidirect |
| 27. #17988327 | C4 | semidirect |
| 28. #17988326 | C4 | semidirect |
| 29. #17988326 | C4 | semidirect |
| 30. #329×C73 | C4 | semidirect |
| 69. #14556502 | C2×C4 | semidirect |
| 70. #14556502 | C2×C4 | semidirect |
| 74. #97×C73 | C2×C4 | semidirect |
| 75. #97×C73 | C2×C4 | semidirect |
| 235. C73 | #8911 | semidirect |
| 258. #329 | #64408 | semidirect |
| 296. #97 | C2×#64408 | semidirect |
| 297. #97 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626474 | 2 |
| #22626061 | 2 |
| #22625869 | 2 |
| #22625854 | 2 |
| #22624808 | 2 |
| #329×D73 | 2 |
| #8911 | 73 |