Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
220 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C107 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C107 |
| prime radical | #493×C107 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C42×C107 ◁ C8×Q8×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C16×C107 | C2 | semidirect |
| 3. C107×#1674 | C2 | semidirect |
| 5. C107×#1371 | C2 | semidirect |
| 6. C107×#1364 | C2 | semidirect |
| 101. #12475 | C107 | direct (N × H) |
| 107. Q8×C16 | C2×C107 | semidirect |
| 108. #1674 | C2×C107 | semidirect |
| 110. #1371 | C2×C107 | semidirect |
| 111. #1364 | C2×C107 | semidirect |
| 113. C107 | #12475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#2240 | 2 |
| Q8×C16×C107 | 2 |
| C107×#1674 | 2 |
| C107×#1668 | 2 |
| C107×#1371 | 2 |
| C107×#1364 | 2 |
| C107×#1361 | 2 |
| #12475 | 107 |