Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #22611725 | C2 | semidirect |
| 3. #22611681 | C2 | semidirect |
| 4. C2×#17988396 | C2 | semidirect |
| 5. #22611551 | C2 | semidirect |
| 6. #22609991 | C2 | semidirect |
| 7. C73×#1383 | C2 | semidirect |
| 183. #1383 | D73 | semidirect |
| 184. C73 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619652 | 2 |
| #22611725 | 2 |
| #22611681 | 2 |
| C2×#17988396 | 2 |
| #22611551 | 2 |
| #22609991 | 2 |
| C73×#1383 | 2 |
| #13391 | 73 |