Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 109 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×#17988700 | C2 | semidirect |
| 3. C2×#17988399 | C2 | semidirect |
| 4. C2×#17988397 | C2 | semidirect |
| 5. #22608031 | C2 | semidirect |
| 6. #22608011 | C2 | semidirect |
| 7. C73×#1975 | C2 | semidirect |
| 12. C2×#14556534 | C4 | semidirect |
| 13. C2×#14556532 | C4 | semidirect |
| 46. C2×#11924003 | C2×C4 | semidirect |
| 55. C2×Q16×C73 | C2×C4 | semidirect |
| 57. C2×D8×C73 | C2×C4 | semidirect |
| 183. #1975 | D73 | semidirect |
| 186. C73 | #13037 | semidirect |
| 213. C2×Q16 | C4×D73 | semidirect |
| 221. C2×D8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989022 | 2 |
| C2×#17988700 | 2 |
| C2×#17988399 | 2 |
| C2×#17988397 | 2 |
| #22608031 | 2 |
| #22608011 | 2 |
| C73×#1975 | 2 |
| #13037 | 73 |