Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626279 | C2 | semidirect |
| 3. C2×#17989512 | C2 | semidirect |
| 5. #22625003 | C2 | semidirect |
| 6. #22624999 | C2 | semidirect |
| 25. #17988372 | C4 | semidirect |
| 26. #17988371 | C4 | semidirect |
| 27. #17988370 | C4 | semidirect |
| 28. #350×C73 | C4 | semidirect |
| 61. #14556531 | C2×C4 | semidirect |
| 65. C2×#11924003 | C2×C4 | semidirect |
| 68. M32×C73 | C2×C4 | semidirect |
| 69. C2×C16×C73 | C2×C4 | semidirect |
| 187. C73 | #12934 | semidirect |
| 207. #350 | #64408 | semidirect |
| 233. M32 | C2×#64408 | semidirect |
| 236. C2×C16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626585 | 2 |
| #22626279 | 2 |
| C2×#17989512 | 2 |
| #22625817 | 2 |
| #22625003 | 2 |
| #22624999 | 2 |
| #22611557 | 2 |
| #12934 | 73 |