Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#17988391 | C2 | semidirect |
| 5. #22608040 | C2 | semidirect |
| 6. #22608026 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 13. #17988859 | C4 | semidirect |
| 51. #14556527 | C2×C4 | semidirect |
| 63. C2×Q16×C73 | C2×C4 | semidirect |
| 184. #2141 | D73 | semidirect |
| 189. C73 | #12997 | semidirect |
| 220. C2×Q16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988859 | 2 |
| #22618528 | 2 |
| C2×#17988391 | 2 |
| C2×#17988372 | 2 |
| #22608040 | 2 |
| #22608026 | 2 |
| C73×#2141 | 2 |
| #12997 | 73 |