Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22620846 | C2 | semidirect |
| 2. #22619391 | C2 | semidirect |
| 3. #22614873 | C2 | semidirect |
| 4. #22608598 | C2 | semidirect |
| 5. #22608323 | C2 | semidirect |
| 6. #22607834 | C2 | semidirect |
| 7. C73×#1502 | C2 | semidirect |
| 58. C4⋊#10596831 | D4 | semidirect |
| 59. C4⋊#10596831 | D4 | semidirect |
| 66. C4⋊Q8×C73 | D4 | semidirect |
| 67. #127×C73 | D4 | semidirect |
| 102. C2×D292 | D8 | semidirect |
| 245. #1502 | D73 | semidirect |
| 248. C73 | #10238 | semidirect |
| 285. C4⋊Q8 | D292 | semidirect |
| 292. #127 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620846 | 2 |
| #22619391 | 2 |
| #22614873 | 2 |
| #22608598 | 2 |
| #22608323 | 2 |
| #22607834 | 2 |
| C73×#1502 | 2 |
| #10238 | 73 |