Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22626949 | C2 | semidirect |
| 4. #22626948 | C2 | semidirect |
| 5. #22626947 | C2 | semidirect |
| 6. C8×#11924040 | C2 | semidirect |
| 48. #11924040 | M16 | semidirect |
| 84. #10596833 | M32 | semidirect |
| 115. C73 | #11409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627128 | 2 |
| C4×#14556687 | 2 |
| #22626949 | 2 |
| #22626948 | 2 |
| #22626947 | 2 |
| C8×#11924040 | 2 |
| #22625132 | 2 |
| #11409 | 73 |