Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22608817 | C2 | semidirect |
| 3. #22608004 | C2 | semidirect |
| 4. #22607892 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. #22607849 | C2 | semidirect |
| 7. C8×D8×C73 | C2 | semidirect |
| 58. D8×C73 | M16 | semidirect |
| 114. C8×D8 | D73 | semidirect |
| 119. C73 | #12073 | semidirect |
| 163. D8 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556532 | 2 |
| #22608817 | 2 |
| #22608004 | 2 |
| #22607892 | 2 |
| #22607891 | 2 |
| #22607849 | 2 |
| C8×D8×C73 | 2 |
| #12073 | 73 |