Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. C2×#17989511 | C2 | semidirect |
| 4. #22626050 | C2 | semidirect |
| 5. #22624997 | C2 | semidirect |
| 6. #22624980 | C2 | semidirect |
| 25. #17988395 | C4 | semidirect |
| 26. #17988394 | C4 | semidirect |
| 27. #17988393 | C4 | semidirect |
| 28. #359×C73 | C4 | semidirect |
| 64. C2×#11924003 | C2×C4 | semidirect |
| 65. #14556527 | C2×C4 | semidirect |
| 68. C2×C16×C73 | C2×C4 | semidirect |
| 69. #108×C73 | C2×C4 | semidirect |
| 185. C73 | #12949 | semidirect |
| 205. #359 | #64408 | semidirect |
| 234. 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 |
|---|---|
| #22626694 | 2 |
| C2×#17989511 | 2 |
| #22626259 | 2 |
| #22626050 | 2 |
| #22624997 | 2 |
| #22624980 | 2 |
| #22611657 | 2 |
| #12949 | 73 |