Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
1006 conjugacy classes of subgroups; only the 510 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 510 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C107 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C107 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ C43×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 26. C4×C8×C107 | Q8 | semidirect |
| 51. C8×C107 | C4⋊Q8 | semidirect |
| 57. C4×C107 | #498 | semidirect |
| 59. #33310 | C107 | direct (N × H) |
| 67. C107 | #33310 | direct (N × H) |
| 89. C4×C8 | Q8×C107 | semidirect |
| 114. C8 | C4⋊Q8×C107 | semidirect |
| 120. C4 | #498×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#498×C107 | 2 |
| C107×#2868 | 2 |
| C107×#1844 | 2 |
| C42×C8×C107 | 2 |
| #33310 | 107 |