Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1080 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 1. #22627081 | C2 | semidirect |
| 2. #22627079 | C2 | semidirect |
| 3. #22627077 | C2 | semidirect |
| 4. #22627070 | C2 | semidirect |
| 6. C23×#10596842 | C22 | semidirect |
| 7. C2×C4⋊#10596842 | C22 | semidirect |
| 10. C2×C22⋊#10596842 | C22 | semidirect |
| 11. C2×C4×#10596842 | C22 | semidirect |
| 12. (C2×#10596842)⋊C4 | C22 | semidirect |
| 43. #14556561 | C8 | semidirect |
| 44. #14556560 | C8 | semidirect |
| 45. #14556559 | C8 | semidirect |
| 47. #120×C73 | C8 | semidirect |
| 75. C23×D73 | C2×C8 | semidirect |
| 84. C22⋊Dic73 | C2×C8 | semidirect |
| 85. #11924005 | C2×C8 | semidirect |
| 86. C24×C73 | C2×C8 | semidirect |
| 88. C22⋊C4×C73 | C2×C8 | semidirect |
| 164. C73 | #23306 | semidirect |
| 192. #120 | #10596842 | semidirect |
| 212. C24 | C2×#10596842 | semidirect |
| 245. C22⋊C4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627081 | 2 |
| #22627079 | 2 |
| #22627077 | 2 |
| #22627070 | 2 |
| #120×#64408 | 2 |
| #23306 | 73 |