Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 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×C103 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C103 |
| prime radical | C103×#3186 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×C22⋊C8×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#2185 | C2 | semidirect |
| 3. C103×#2001 | C2 | semidirect |
| 4. C103×#1347 | C2 | semidirect |
| 5. C103×#1314 | C2 | semidirect |
| 6. C22×Q16×C103 | C22 | semidirect |
| 17. C22⋊C16×C103 | C22 | semidirect |
| 18. #340×C103 | C22 | semidirect |
| 98. C23×C103 | SD32 | semidirect |
| 150. #12105 | C103 | direct (N × H) |
| 159. #2185 | C2×C103 | semidirect |
| 160. #2001 | C2×C103 | semidirect |
| 161. #1347 | C2×C103 | semidirect |
| 162. #1314 | C2×C103 | semidirect |
| 163. C103 | #12105 | direct (N × H) |
| 164. C22×Q16 | C22×C103 | semidirect |
| 175. C22⋊C16 | C22×C103 | semidirect |
| 176. #340 | C22×C103 | semidirect |
| 256. C23 | SD32×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#3186 | 2 |
| C103×#2185 | 2 |
| C103×#2001 | 2 |
| C103×#1347 | 2 |
| C103×#1314 | 2 |
| #12105 | 103 |