Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22619971 | C2 | semidirect |
| 4. #22608494 | C2 | semidirect |
| 5. #22608359 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 93. C2×D292 | Q16 | semidirect |
| 220. #1286 | D73 | semidirect |
| 221. C73 | #10002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619971 | 2 |
| #22619730 | 2 |
| #22615290 | 2 |
| #22608494 | 2 |
| #22608359 | 2 |
| #22608323 | 2 |
| C73×#1286 | 2 |
| #10002 | 73 |