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. #22608496 | C2 | semidirect |
| 5. #22608361 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 119. C2×D4×C73 | Q16 | semidirect |
| 221. C73 | #10002 | semidirect |
| 307. C2×D4 | Dic292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619971 | 2 |
| #22619728 | 2 |
| #22615285 | 2 |
| #22608496 | 2 |
| #22608361 | 2 |
| #22607790 | 2 |
| C73×#1478 | 2 |
| #10002 | 73 |