Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612074 | C2 | semidirect |
| 4. C8×Dic292 | C2 | semidirect |
| 5. #22607985 | C2 | semidirect |
| 7. C73×#1367 | C2 | semidirect |
| 51. Dic292 | SD16 | semidirect |
| 90. C8×C73 | SD32 | semidirect |
| 115. #1367 | D73 | semidirect |
| 118. C73 | #12417 | semidirect |
| 202. C8 | #14556536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612074 | 2 |
| #22611972 | 2 |
| #22609523 | 2 |
| C8×Dic292 | 2 |
| #22607985 | 2 |
| #22607978 | 2 |
| C73×#1367 | 2 |
| #12417 | 73 |