Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22626948 | C2 | semidirect |
| 36. C8×D73 | C16 | semidirect |
| 55. C8×C73 | C2×C16 | semidirect |
| 56. #10596831 | C2×C16 | semidirect |
| 71. D73 | #1312 | semidirect |
| 75. C73 | C2×#1312 | semidirect |
| 128. C8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556686 | 2 |
| #22626948 | 2 |
| C8×#11924036 | 2 |
| C2×#1312 | 73 |