Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
628 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#124×C43 | C2 | semidirect |
| 2. C2×C4×D4×C43 | C2 | semidirect |
| 3. C43×#397 | C2 | semidirect |
| 4. C43×#393 | C2 | semidirect |
| 5. C43×#392 | C2 | semidirect |
| 6. C43×#392 | C2 | semidirect |
| 7. C43×#386 | C2 | semidirect |
| 8. C43×#383 | C2 | semidirect |
| 52. C42×C43 | D4 | semidirect |
| 102. #2631 | C43 | direct (N × H) |
| 109. C2×#124 | C2×C43 | semidirect |
| 110. C2×C4×D4 | C2×C43 | semidirect |
| 111. #397 | C2×C43 | semidirect |
| 112. #393 | C2×C43 | semidirect |
| 113. #392 | C2×C43 | semidirect |
| 114. #392 | C2×C43 | semidirect |
| 115. #386 | C2×C43 | semidirect |
| 116. #383 | C2×C43 | semidirect |
| 117. C43 | #2631 | direct (N × H) |
| 161. C42 | D4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C43 | 2 |
| C2×C4×D4×C43 | 2 |
| C43×#397 | 2 |
| C43×#393 | 2 |
| C43×#392 | 2 |
| C43×#386 | 2 |
| C43×#383 | 2 |
| #2631 | 43 |