Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#17989025 | C2 | semidirect |
| 2. #22619651 | C2 | semidirect |
| 3. #22619579 | C2 | semidirect |
| 4. C2×#17988401 | C2 | semidirect |
| 5. #22611668 | C2 | semidirect |
| 6. #22608046 | C2 | semidirect |
| 7. C73×#2117 | C2 | semidirect |
| 42. C2×Dic292 | D4 | semidirect |
| 50. C2×D584 | D4 | semidirect |
| 60. #14556527 | D4 | semidirect |
| 78. M32×C73 | D4 | semidirect |
| 217. #2117 | D73 | semidirect |
| 219. C73 | #13310 | semidirect |
| 283. M32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989025 | 2 |
| #22619651 | 2 |
| #22619579 | 2 |
| C2×#17988401 | 2 |
| #22611668 | 2 |
| #22608046 | 2 |
| C73×#2117 | 2 |
| #13310 | 73 |