Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22608002 | C2 | semidirect |
| 4. #22607895 | C2 | semidirect |
| 6. #22607848 | C2 | semidirect |
| 7. C8×Q16×C73 | C2 | semidirect |
| 26. #14556534 | C8 | semidirect |
| 54. #11924003 | C2×C8 | semidirect |
| 57. Q16×C73 | C2×C8 | semidirect |
| 107. C8×Q16 | D73 | semidirect |
| 113. C73 | #12043 | semidirect |
| 154. Q16 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556534 | 2 |
| C8×D584 | 2 |
| #22608002 | 2 |
| #22607895 | 2 |
| #22607891 | 2 |
| #22607848 | 2 |
| C8×Q16×C73 | 2 |
| #12043 | 73 |