Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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 |
|---|---|---|
| 1. C22×#14556583 | C2 | semidirect |
| 3. C2×#17988942 | C2 | direct (N × H) |
| 4. C22×#14556516 | C2 | semidirect |
| 6. C22×C4×C8×C73 | C2 | semidirect |
| 10. C2×#14556583 | C22 | semidirect |
| 16. #17988942 | C22 | direct (N × H) |
| 17. C2×#14556516 | C22 | semidirect |
| 21. C2×C4×C8×C73 | C22 | semidirect |
| 32. #14556583 | C23 | semidirect |
| 39. #14556516 | C23 | semidirect |
| 47. C4×C8×C73 | C23 | semidirect |
| 99. C22×C73 | #488 | semidirect |
| 112. C2×C73 | C2×#488 | semidirect |
| 121. C22×C4×C8 | D73 | semidirect |
| 122. C73 | C22×#488 | semidirect |
| 137. C2×C4×C8 | C2×D73 | semidirect |
| 163. C4×C8 | C22×D73 | semidirect |
| 218. C22 | #17988942 | direct (N × H) |
| 228. C2 | C2×#17988942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556583 | 2 |
| C22×#14556579 | 2 |
| C2×#17988942 | 2 |
| C22×#14556516 | 2 |
| C22×#14556513 | 2 |
| C22×C4×C8×C73 | 2 |
| C22×#488 | 73 |