Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 96 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×D8×#64408 | C2 | semidirect |
| 2. C2×#17989499 | C2 | semidirect |
| 3. C2×#17989499 | C2 | semidirect |
| 4. #22626078 | C2 | semidirect |
| 5. #22624989 | C2 | semidirect |
| 6. #22624968 | C2 | semidirect |
| 22. C2×D1168 | C4 | semidirect |
| 23. C2×#14556532 | C4 | semidirect |
| 24. C2×#14556532 | C4 | semidirect |
| 28. C2×D16×C73 | C4 | semidirect |
| 53. C2×D584 | C2×C4 | semidirect |
| 68. C2×#11924003 | C2×C4 | semidirect |
| 72. C2×D8×C73 | C2×C4 | semidirect |
| 74. C2×C16×C73 | C2×C4 | semidirect |
| 113. D584 | C22⋊C4 | semidirect |
| 129. D8×C73 | C22⋊C4 | semidirect |
| 161. C2×#64408 | D16 | semidirect |
| 239. C73 | #13012 | semidirect |
| 248. C2×D16 | #64408 | semidirect |
| 277. C2×D8 | C2×#64408 | semidirect |
| 298. C2×C16 | C2×#64408 | semidirect |
| 342. D8 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#64408 | 2 |
| C2×#17989499 | 2 |
| #22626078 | 2 |
| #22624989 | 2 |
| #22624968 | 2 |
| C2×D16×D73 | 2 |
| #13012 | 73 |