Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
948 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 112 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×#17989504 | C2 | semidirect |
| 2. C2×#17989503 | C2 | semidirect |
| 3. #22626159 | C2 | semidirect |
| 4. #22625807 | C2 | semidirect |
| 6. C2×#14556666 | C22 | semidirect |
| 7. C2×#14556659 | C22 | semidirect |
| 16. C2×#14556613 | C4 | semidirect |
| 22. C2×Q16×D73 | C4 | semidirect |
| 24. C2×D8×D73 | C4 | semidirect |
| 26. C2×#135×C73 | C4 | semidirect |
| 121. Dic292 | C22⋊C4 | semidirect |
| 127. D584 | C22⋊C4 | semidirect |
| 146. Q16×C73 | C22⋊C4 | semidirect |
| 149. D8×C73 | C22⋊C4 | semidirect |
| 223. C2×D73 | #360 | semidirect |
| 247. C73 | #12735 | semidirect |
| 256. C2×#135 | #64408 | semidirect |
| 369. Q16 | C22⋊#64408 | semidirect |
| 378. D8 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989504 | 2 |
| C2×#17989503 | 2 |
| #22626159 | 2 |
| #22625807 | 2 |
| C2×#135×D73 | 2 |
| #12735 | 73 |