Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
690 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#17989708 | C2 | semidirect |
| 2. #22627147 | C2 | semidirect |
| 3. D4×#11924040 | C2 | semidirect |
| 4. #22627120 | C2 | semidirect |
| 5. #22627102 | C2 | semidirect |
| 6. C4×#14556686 | C2 | semidirect |
| 28. #14556686 | D4 | semidirect |
| 108. C4×C73 | #504 | semidirect |
| 125. C73 | #33434 | semidirect |
| 230. C4 | #17989708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989708 | 2 |
| #22627147 | 2 |
| D4×#11924040 | 2 |
| #22627120 | 2 |
| #22627102 | 2 |
| C4×#14556686 | 2 |
| #22626653 | 2 |
| #33434 | 73 |