Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
954 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 118 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×#17989500 | C2 | semidirect |
| 2. C2×#17989499 | C2 | semidirect |
| 3. #22626156 | C2 | semidirect |
| 4. #22625808 | C2 | semidirect |
| 15. C2×#14556614 | C4 | semidirect |
| 16. C2×#14556613 | C4 | semidirect |
| 19. C2×#14556610 | 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 |
| 253. C73 | #12733 | semidirect |
| 262. C2×#135 | #64408 | semidirect |
| 375. Q16 | C22⋊#64408 | semidirect |
| 384. D8 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989500 | 2 |
| C2×#17989499 | 2 |
| #22626156 | 2 |
| #22625808 | 2 |
| C2×#135×D73 | 2 |
| #12733 | 73 |