Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2590 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1464 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #64408 |
| commutator, hypocenter | C73 | C24×C16 |
| Frattini | C4 | C24×#64408 |
| Fitting | C23×C8×C73 | C4 |
| socle | C24×C73 | C2×C8 |
| prime radical | C24×D73 | C8 |
| cosocle | #10596831 | C25 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14556664 | C2 | direct (N × H) |
| 2. C23×#11924031 | C2 | semidirect |
| 4. C2×#14556664 | C22 | direct (N × H) |
| 5. C22×#11924031 | C22 | semidirect |
| 11. #14556664 | C23 | direct (N × H) |
| 12. C2×#11924031 | C23 | semidirect |
| 23. #11924031 | C24 | semidirect |
| 24. C23×D73 | C16 | semidirect |
| 37. C23×C73 | C2×C16 | semidirect |
| 39. C22×D73 | C2×C16 | semidirect |
| 49. C22×C73 | C22×C16 | semidirect |
| 51. C2×D73 | C22×C16 | semidirect |
| 57. C2×C73 | C23×C16 | semidirect |
| 59. D73 | C23×C16 | semidirect |
| 63. C73 | C24×C16 | semidirect |
| 99. C23 | #14556664 | direct (N × H) |
| 111. C22 | C2×#14556664 | direct (N × H) |
| 117. C2 | C22×#14556664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556664 | 2 |
| C23×#11924031 | 2 |
| C23×C8×D73 | 2 |
| C24×C16 | 73 |