Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#17988417 | C2 | semidirect |
| 3. C2×#17988403 | C2 | semidirect |
| 6. #22608039 | C2 | semidirect |
| 7. C2×#358×C73 | C2 | semidirect |
| 167. C2×#358 | D73 | semidirect |
| 171. C73 | #13394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988859 | 2 |
| C2×#17988417 | 2 |
| C2×#17988403 | 2 |
| #22611544 | 2 |
| #22609996 | 2 |
| #22608039 | 2 |
| C2×#358×C73 | 2 |
| #13394 | 73 |