Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988709 | C2 | semidirect |
| 3. C2×#17988401 | C2 | semidirect |
| 4. #22610805 | C2 | semidirect |
| 5. #22608029 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 7. C2×#360×C73 | C2 | semidirect |
| 12. C2×#14556534 | C4 | semidirect |
| 13. C2×#14556532 | C4 | semidirect |
| 103. Q16×C73 | C22⋊C4 | semidirect |
| 107. D8×C73 | C22⋊C4 | semidirect |
| 181. C2×#360 | D73 | semidirect |
| 185. C73 | #13040 | semidirect |
| 265. Q16 | #11924005 | semidirect |
| 273. D8 | #11924005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989022 | 2 |
| C2×#17988709 | 2 |
| C2×#17988401 | 2 |
| #22610805 | 2 |
| #22608029 | 2 |
| #22608010 | 2 |
| C2×#360×C73 | 2 |
| #13040 | 73 |