Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22608829 | C2 | semidirect |
| 4. #22608005 | C2 | semidirect |
| 5. #22607896 | C2 | semidirect |
| 7. C8×C16×C73 | C2 | semidirect |
| 67. C16×C73 | M16 | semidirect |
| 84. C8×C73 | SD32 | semidirect |
| 112. C8×C16 | D73 | semidirect |
| 113. C73 | #12082 | semidirect |
| 173. C16 | #11924011 | semidirect |
| 192. C8 | #14556536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556536 | 2 |
| #22608829 | 2 |
| #22608817 | 2 |
| #22608005 | 2 |
| #22607896 | 2 |
| #22607893 | 2 |
| C8×C16×C73 | 2 |
| #12082 | 73 |