Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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×#17988498 | C2 | direct (N × H) |
| 3. C22×#14556498 | C2 | semidirect |
| 4. C24×Q8×C73 | C2 | semidirect |
| 9. #17988498 | C22 | direct (N × H) |
| 10. C2×#14556498 | C22 | semidirect |
| 12. C23×Q8×C73 | C22 | semidirect |
| 16. C24×D73 | Q8 | semidirect |
| 23. #14556498 | C23 | semidirect |
| 27. C22×Q8×C73 | C23 | semidirect |
| 36. C23×D73 | C2×Q8 | semidirect |
| 66. C22×D73 | C22×Q8 | semidirect |
| 74. C22×C73 | #393 | semidirect |
| 88. C2×C73 | C2×#393 | semidirect |
| 93. C24×Q8 | D73 | semidirect |
| 97. C73 | C22×#393 | semidirect |
| 100. C23×Q8 | C2×D73 | semidirect |
| 114. C22×Q8 | C22×D73 | semidirect |
| 171. C22 | #17988498 | direct (N × H) |
| 181. C2 | C2×#17988498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924005 | 2 |
| C2×#17988498 | 2 |
| C22×#14556498 | 2 |
| C24×Q8×C73 | 2 |
| C22×#393 | 73 |