Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1174 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22620858 | C2 | semidirect |
| 3. #22615136 | C2 | semidirect |
| 4. #22608902 | C2 | semidirect |
| 5. #22608427 | C2 | semidirect |
| 6. C73×#1461 | C2 | semidirect |
| 109. C2×Q8×C73 | SD16 | semidirect |
| 186. #1461 | D73 | semidirect |
| 187. C73 | #18402 | semidirect |
| 267. C2×Q8 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623702 | 2 |
| #22620858 | 2 |
| #22615136 | 2 |
| #22608902 | 2 |
| #22608427 | 2 |
| C73×#1461 | 2 |
| #18402 | 73 |