Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611764 | C2 | semidirect |
| 3. #22608001 | C2 | semidirect |
| 4. #22607887 | C2 | semidirect |
| 5. C8×C16×C73 | C2 | semidirect |
| 48. C16×C73 | D8 | semidirect |
| 61. C8×C73 | M32 | semidirect |
| 84. C8×C16 | D73 | semidirect |
| 85. C73 | #12039 | semidirect |
| 128. C16 | D584 | semidirect |
| 142. C8 | #14556530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611764 | 2 |
| C8×D584 | 2 |
| #22608001 | 2 |
| #22607887 | 2 |
| C8×C16×C73 | 2 |
| #12039 | 73 |