Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
774 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22610766 | C2 | semidirect |
| 3. #22609875 | C2 | semidirect |
| 4. #22608446 | C2 | semidirect |
| 5. #22607837 | C2 | semidirect |
| 6. #22607817 | C2 | semidirect |
| 7. C73×#2341 | C2 | semidirect |
| 8. C2×#14556616 | C4 | semidirect |
| 14. #17988588 | C4 | semidirect |
| 155. Q8×C73 | #99 | semidirect |
| 239. #2341 | D73 | semidirect |
| 245. C73 | #9368 | semidirect |
| 393. Q8 | #14556505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619183 | 2 |
| #22610766 | 2 |
| #22609875 | 2 |
| #22608446 | 2 |
| #22607837 | 2 |
| #22607817 | 2 |
| C73×#2341 | 2 |
| #9368 | 73 |