Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C107 |
| prime radical | C107×#2206 | C2 |
| 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 |
|---|---|---|
| 1. C107×#3393 | C2 | semidirect |
| 2. C107×#2248 | C2 | semidirect |
| 4. C107×#1668 | C2 | semidirect |
| 5. C107×#1362 | C2 | semidirect |
| 6. C107×Q8⋊C16 | C2 | semidirect |
| 7. C107×#1331 | C2 | semidirect |
| 132. #12331 | C107 | direct (N × H) |
| 138. #3393 | C2×C107 | semidirect |
| 139. #2248 | C2×C107 | semidirect |
| 141. #1668 | C2×C107 | semidirect |
| 142. #1362 | C2×C107 | semidirect |
| 143. Q8⋊C16 | C2×C107 | semidirect |
| 144. #1331 | C2×C107 | semidirect |
| 145. C107 | #12331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3393 | 2 |
| C107×#2248 | 2 |
| C107×#2206 | 2 |
| C107×#1668 | 2 |
| C107×#1362 | 2 |
| C107×Q8⋊C16 | 2 |
| C107×#1331 | 2 |
| #12331 | 107 |