Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 558 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. C2×#17989030 | C2 | semidirect |
| 2. C2×#17989027 | C2 | semidirect |
| 4. C2×#17988396 | C2 | semidirect |
| 5. #22610800 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C2×#360×C73 | C2 | semidirect |
| 47. C2×Dic292 | D4 | semidirect |
| 67. #14556531 | D4 | semidirect |
| 84. M32×C73 | D4 | semidirect |
| 225. C2×#360 | D73 | semidirect |
| 228. C73 | #13342 | semidirect |
| 300. M32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989030 | 2 |
| C2×#17989027 | 2 |
| #22620374 | 2 |
| C2×#17988396 | 2 |
| #22610800 | 2 |
| #22608014 | 2 |
| C2×#360×C73 | 2 |
| #13342 | 73 |