Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22611651 | C2 | semidirect |
| 5. #22608039 | C2 | semidirect |
| 6. #22608027 | C2 | semidirect |
| 7. C2×#358×C73 | C2 | semidirect |
| 13. #17988859 | C4 | semidirect |
| 51. #14556527 | C2×C4 | semidirect |
| 64. C2×Q16×C73 | C2×C4 | semidirect |
| 185. C2×#358 | D73 | semidirect |
| 189. C73 | #12997 | semidirect |
| 220. C2×Q16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988859 | 2 |
| #22618527 | 2 |
| #22611651 | 2 |
| C2×#17988370 | 2 |
| #22608039 | 2 |
| #22608027 | 2 |
| C2×#358×C73 | 2 |
| #12997 | 73 |