Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22611833 | C2 | semidirect |
| 4. #22607909 | C2 | semidirect |
| 6. C8×#11924003 | C2 | semidirect |
| 7. C73×#1367 | C2 | semidirect |
| 47. #11924017 | C16 | semidirect |
| 59. #11924003 | SD16 | semidirect |
| 80. Dic146 | C2×C16 | semidirect |
| 84. C8×C73 | C2×C16 | semidirect |
| 109. #1367 | D73 | semidirect |
| 113. C73 | C16×SD16 | semidirect |
| 192. C8 | C16×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611833 | 2 |
| #22611750 | 2 |
| C8×#11924017 | 2 |
| #22607909 | 2 |
| #22607885 | 2 |
| C8×#11924003 | 2 |
| C73×#1367 | 2 |
| C16×SD16 | 73 |