Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
696 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 255 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. #22610646 | C2 | semidirect |
| 4. #22610485 | C2 | semidirect |
| 6. #22610074 | C2 | semidirect |
| 7. C73×#1842 | C2 | semidirect |
| 29. #14556585 | C8 | semidirect |
| 60. #11924007 | C2×C8 | semidirect |
| 75. C42×C73 | C2×C8 | semidirect |
| 124. #1842 | D73 | semidirect |
| 126. C73 | #23375 | semidirect |
| 194. C42 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556585 | 2 |
| #22610646 | 2 |
| #22610536 | 2 |
| #22610485 | 2 |
| #22610107 | 2 |
| #22610074 | 2 |
| C73×#1842 | 2 |
| #23375 | 73 |